I don't know if what I've said makes any sense.  I am just speculated based of my very limited understanding of special relativity.  Still some people on this site seem to understand this better then I do so I wanted to see what they think.  

The problems(if there really is a problem) is exactly what you said.  The longer you have a high velocity the greater the effects of time dilation.  It seems that you can have exact same acceleration with different values of X.  The way I understand it General Relativity is the solution for the twin paradox, and General Relativity relies in some way on acceleration. If what I understand is correct then I can't understand how the same acceleration can counteract different amounts of time dilation.  

It is possible I'm just missing, or failing to understand something.  If so hopefully someone will explain were I have gone wrong.  

Eh, I have some knowledge of relativity. I'm not sure if I understand what you're asking here though.

I assume that the two spaceships are traveling in opposite directions? When you say they come to 'rest,' you are referring to a third reference frame. If their motion is the same but in opposite directions, then they should observe the same period of time to have elapsed when they meet in this rest frame. What is the supposed paradox here? The farther they travel, the less time that will have elapsed in their reference frames relative to the rest frame because they will have traveled faster relative to the rest frame and/or for the longer period of time.

The adjustment that resolves the 'paradox' occurs while they are undergoing acceleration/deceleration.

The apparent rate of time passing as seen from the other, when either or both are undergoing acceleration, and therefore described under General Relativity, gets much more complicated than for Special Relativity.

I haven't got time to chase this up in detail right now, but I looked into it a bit when this came up before, and it is all in the velocity changes, which prevents a paradox arising.

I think the 'problem' is reconciling the fact that each 'twin' will see the other aging much slower than themselves during the constant speed sections of the fight, as per SR, so how do they end up the same when they get back together?

It has to be in the acceleration stages that it all sorts out.

That's it exactly.  Where does it sort out?  It has to sort out somehow, and the most likely place is during the accelerations.

Trying to understand this better I've created two scenarios.  In both scenarios the spacecraft are programed to accelerate for the same period of time.   The difference between the two scenarios is how long the space craft are allowed to coast without accelerating.  In scenario one the space craft is allowed to coast 10 light years.  In scenario two the space craft is allowed to coast 100 light years(Scenario 1 x=10, scenario 2 x=100).   The higher the value of X the greater the total effects from time dilation, and the more time that must be made up for during the acceleration parts.  

The difference between X=10 and X=100 can't be sorted out by acceleration A1 because A1 is the same for both scenarios.  I doubt it can be sorted out by acceleration A3 because I don't think that A3 is even really necessary for this thought experiment.  That only leave acceleration A2.  In scenario 1 and scenario 2 A1 and V1 are the same.  The only difference between the two is X.  This makes me wonder if distance has some affect on how we view the effects of acceleration.  

In regards to acceleration the only other possibility that I can think of has to do with differences between when the two twins view that acceleration events as happening.  Fred will not necessarily view Bob experience A2 while he is experiences A2.  Just as Bob not necessarily view Fred experience A2 while he is experiencing A2.  Perhaps the time difference can be made up through difference the two twins experience over exactly when the various events are happening.   It hard for me to imagine that this could account for vary large values of X.  I'll have to think about it more.  

I'm not sure what you guys are seeing, that I'm not.

Help me out here...

I'm modeling this now as if the 2 twins are both experiencing the same thing, in crafts that are right alongside each other. If they were to look out through a window at each other, while any of this accelerating/coasting etc, is going on, they wouldn't 'see' the other any differently than if they then glanced in the mirror at themselves.

IOW, 'relative' to space/time, they're the same, just as if they were sitting next to each other on a park bench (relative to space/time).

Imagine that Fred and Bob have clocks with them that start out at 0.  When the trip ends both Fred and Bobs clocks will read 50 (of some arbitrary time unit).  During the trip when his clock says 20 Fred observes Bob.  What Fred sees is exactly the same thing as Bob would see if he observed Fred when his clock said 20.   If Fred was able to read Bob's clock while observing him he wold likely see a number other then 20.   Lets say that the number Fred saw was 30 (Even though I don't really know what it would be).  If that was the case Bob would also see 30 while reading Fred clock.  

Fred and Bob would see exactly the same things while observing each other, but they wouldn't see things happening to their twin at the same time they were happening to them.  In other words if they could observe what was on their twins clock most of the time it would say something different from what was on their own clock.  

OK, you have overcomplicated the matter and that is just adding to your confusion. Before I get to that, I want to state that any teacher who invokes general relativity to explain away any of the issues from special relativity probably does not understand either one and is just regurgitating a bad idea to cover their ignorance on the matter.

Time dilation happens for any velocity but for regular experience, the effect is too small to be worth taking into account. For example, a theoretical astronaut a hundred years from now may spend his whole career running around the solar system at 10% of c but after 30 years, he will return to earth only a day younger than his brother who never left earth.

Anyway, it would be much easier to just consider two brothers with one staying on the earth and the other taking off into space. If you add a third person into the mix, then you just have another entity to solve for. You can do that if you want to but it will not make the case for two entities clearer.

Here is one way to go about this:

Let's take two identical clocks and put one of them on the space ship. Both clocks should have radio gear so that they may be monitored one from the other. Here is the thing, for a distant clock, you have to calculate the time that it takes for the radio waves to travel to the other clock. So if one clock is on the moon, even though there is not enough relative motion to produce measurable time dilation, the moon clock will seem to be about two seconds late from the position of an observer on the earth and vice versa.

Here is where this starts to get interesting. If the clock is on a space ship heading away from the earth at a constant speed, then the distance the radio waves must travel and the travel time both are going to be increasing steadily. Because of this, the clock on the space ship will seem to be slower. However, from the pilot's POV, it is the clock back on the earth that seems to have slowed down.

If the space ship was traveling towards the earth, then the two brothers would experience the clocks as ticking faster than usual. One of the key factors that most people miss out on is that in any case, time is always proceeding forward. Just because the approaching clock seems to be faster than the receding one does not mean that you get back the time that was lost while heading on the outbound leg of the journey. The total number of times that the clock ticks are what you have to take into account more so than the rate at which they tick.

I thought that's what I said... where was I wrong? 

Yup, I stand correct it.  

Sorry for being dense here, but what is the paradox exactly? Are you asking about the reconciliation of clocks? or why one is slower than the other when they should be the same? I'm not clear on what's not clear.

OK, you are going about this wrong. What are you measuring when you record the ticking of the clock?

Just for grins, let me say that the ticking is some form of information which happens to be sensitive to the changing distance between the two reference frames. As they close on each other, the ticking has to come in faster because of the decreasing distance.

Let's consider, instead of a ticking clock, a pure sine wave in the audio band. If the emitting object is approaching, then the frequency will be increased and as the object is receding, the frequency will be decreased. It is a simple Doppler shift here.

I see what you are trying to do. The only thing is that just because you can make assumptions does not mean that they are warranted.

One problem is that you have made the assumption of a central point which is a stationary reference. Well, there really is no such thing. Thought experiments may posit such but they may not hold true if you change one of the parameters. That can bork your assumptions to the point where the whole exercise breaks down.

In order to work the way that you are going, your model needs to have a third person who remains at the stationary reference. Then you reconcile the clocks of both astronauts to that third person. In that case, both of the astronauts show the same amount of time dilation in respect to the third person. However, by adding the second astronaut, you now have the additional complication of having to reconcile the clocks between the two of them.

Let me change one of your free parameters and perhaps you will see how this changes things. You have made the assumption that the two astronauts are moving on courses which are 180 degrees apart, basically, they are moving on the same line and in opposite directions. In my restatement, the two astronauts are not moving on the same line but in fact, the headings are 90 degrees apart. If that is not clear, then add in a third astronaut who is moving at right angles to the other two.

Assuming that the helm control is identical fr every astronaut, then the time dilation relative to the stationary observer must be the same for as many astronauts as you care to use. However, when you try to reconcile all of the clocks, what is going to come out? Remember that the astronaut moving at right angles is going to have a different relative velocity to each of the first two than they will have to each other.