Thank you.  This could be a good idea.  The only problem is that I have never been in Mosque nor in Temple.  Actually, we are Christians ... by tradition and we even have baptized our daughter when she was a few months old.  Your approach would readily work for us and my daughter if there were a Russian orthodox Church anywhere near our town.  Mosque would actually work too, I know one, and I know quite a few people who go there.  It will take a little bit more learning and preparation though.  What I mean, my daughter knows who is Zeus and a few other Greek gods, Invisible Pink Unicorn, and now we are learning about Flying Spaghetti Monster, but she has no clue yet about Jesus, Allah, Buddha, Yahweh, etc.

Little girls are the cruelest creatures on earth.  Speaking as an ex-little girl.  It is all about belonging to the group or clique.  The little girls in your area mostly all go to church, so church going is part of being part of the group.  I am not much help in that respect as I never did belong to any of the popular girl cliques.  I was usually a member of the nerd/wallflower clique.  I would make a prediction that even if your daughter went to the popular girl church, being friends would be fraught with the usual fights and fall outs, kiss and be friends again that all little girls do.

And it will always be your fault.  Sorry.  No matter what you do.  Let her go to church, don't discuss your own religious views and she has a fight with her friend and it will be your fault.  Don't let her go and she doesn't have the other girl as her friend and it is all your fault.  Let her go, but let everyone know you are an atheist so their parents ostracize her and it is all your fault.  Let her go, but let everyone know you are an atheist so their parents try to convert you through her and it will be all your fault whether you go or not go to church.  But then, even if there was no church issue, you and your daughter will go through times where no matter what you do, as her father, her problems are all your fault.

My recommendation is to do what you personally are comfortable with and realize this will pass.  If you are true and honest to yourself, eventually your daughter will grow up and love you in part for your steadfastness and loyalty to your ideals.  In the meantime, whatever you decide to do, continue with teaching her about the different irrational beliefs people hold.  Including christianity.

ROFL, gotta love kids honesty, I'd give a pretty penny to see their faces. I was asked to leave a church once when I was six after arguing with the Sunday school teacher that it would have been impossible for Noah to build an ark big enough for two of every animal. Pretty sad for Christians when they can be stumped by a kid. I am hesitant to give any parenting advice since I don't have any kids or plans to have any, but I went to several different churches with various friends while growing up and if anything it only made me more of an atheist. I never got any free ice cream though...

Sounds like your daughter has a pretty good head on her and getting brainwashed probably wouldn't be much of a danger. Although, her mouth might get her banned from seeing some friends and I don't know how big of a town you live in but if it is a smaller one I could see that becoming a problem. 

That reminds me... Some of my neighbours are Evangelical fundies. When I was a kid I attended a lot their activities, because they're all classmates and childhood friends of my mom, we knew their kids too... They're so happy about their church, communion and so on. During communism it was forbidden to gather religionally in privacy, only at a church with priest who was under control of the police. Having and reading a Bible on 2-year mandatory military service was even worse, that could get a private to jail for some days. So they felt really like Christian martyrs, must have done them good (besides some gastritic ulcers) and now they enjoy already 20 years of freedom.

In the end of summer, they have a little 3 days festival with Christian bands, sketches, and a film. I go mainly for the film, but also for a "tearoom" after that. I drink tea, mind my own business and always someone talks to me. We make a small talk, and every time I'm a fisher of sorts, i prey for the innocent little ichthyses that always get on the hook, always ask me if I believe in God. I usually explain them how fake their Bible is, with council of Nicea and two councils of Constantinopolis, what the Christianity originally was (teaching of mystical Jewish sect) and what is it now after several emperors, popes and kings edited it. (Scientology for poor people) Then I explain some other cultures' religional concepts and how similar they are to Bible, specially the teachings of mystical sects. If there's enough of time I describe how much is for example reincarnation much more logical and just than eternal damnation or eternal heaven. Between that, it's pure bliss, pure fun. I love how their eyes seem almost falling out. I love when they ask questions.

No, they won't throw me away, they always gather around to listen. I don't like too many people around, though. They're young people, I don't waste time with the old, they're not going anywhere from this business. I rather play safe with them. No, there is no throwing anyone out of anywhere, we're all neighbours and locals. If anything, I could always say that they started, they asked first.
It's just... well, maybe I should somehow become less expressive, less shining in the company and less overwhelming. I always try to be polite and user-friendly, but it's not enough, mom says. I guess it will be enough when my dear Christians will stop having these faces when I say something. It might save my life from lynching if I ever go to America.

But this is all somewhat off topic, because here I have not yet seen that people would try to convert other parents with kids. It's just a group of less or more fundy families that like to have their own church and unchanging doctrine for like past 50 years. Their own kids are rather unfortunate in direct proportion to their amount of faith. You know, faith and complete ignorance of the world makes them simple-minded and weak-willed, brought up for total obedience to parental authorities. Parents can do anything with them, and they do bad things, like forbidding them everything. (like travel by bus to school) Or if the children are grown up, we have a case that their dad took a big financial loan with his children as guarantees. He just told them:

This isn't a helpful comment, but I just can't get past them luring in kids with free ice cream. It sounds like they're borrowing their tactics from sexual predators...or maybe "borrowing" is the wrong word.

I concur!  Where can we donate to fund carx's sterilization?

I am very nearly Carx's polar opposite- which also goes to show how much atheism is not an ideology.

This is what I would teach my children.

1. Gods don't exist; people usually don't choose to believe in them, but are born into it, and it's very hard to think one's way out of something one didn't think oneself into.  It's like a disease, and religious people should have our sympathies and help- unless they're being jack asses, in which case just avoid them like you would any jerk.
2. People all want to do right by themselves, but we're all also very selfish by nature, so it's a difficult to do the right thing while sacrificing self-service.  To remedy the contradiction, people make up rationalizations, which is a kind of internal dishonesty, and hide the truth from themselves when they want to be self serving.  We're all vulnerable to this tendency, and it's only through learning critical thinking that we can question ourselves and correct our rationalizations.  Not all people have learned how to do that, but you can teach them if you're very patient.  It's hard to unlearn habits, though, so you do have to be very patient.
3.  It's never O.K. to lie unless your life is in danger.  Lying for profit is a disturbing kind of emotional prostitution, and you'll never respect your ideals if you do.  Most people don't understand this, and have become so accustomed to lying that to everybody, including themselves with their rationalizations, that they don't even understand what's real.
4.  There are billions of people in the world, and you can go anywhere, and be anything you want- and meet any kind of person you can imagine and have the best friends you could ever hope for.  Don't settle for less, and never sacrifice a part of yourself to do so.  And most importantly, don't be afraid to let go when you need to- you will always have new friends.
5.  Our relationships with others are the most important things in life.  Yes, you will be hurt sometimes- and hurt badly; it may feel like the world is ending- but it will always get better, and you'll have great joy too.  Avoiding happiness for fear of pain is only as practical as avoiding life itself- cherish all of your experiences and relationships, because they are your life.

To the OP:

It may be hard to hear, but a child's peers define who that child will grow up to be (and largely how emotionally traumatized) much more than the parents do.  A child can forget old friends quickly and make new ones.

Depending on how much you're concerned about your daughter, you should consider moving to a place better suited to her childhood.

If I had a child, I would not rest in seeking friends for said child who would be good influences.

Of course, that's my answer to most things:  Move.  For me, it's profoundly simple.  Some people are not willing to pick up so quickly (often it has to do with too much stuff, which is more of a prison for than a compliment to life)