What's your attachment to that particular church? If you've got family going... and have gone all of your life... stuff like that, I can understand the attachment. But, God is everywhere. Could you find another church of your denomination or a non-denominational church that better suites your family needs? There are a lot ot churches that have huge children's ministries for all ages.
Priorities: What's more important: Being faithful to the group of people that makes up your church and then, just dropping out, because you just can't make it happen? Or being faithful to God (who instructs us in his word to be a part of a community of believers), and diligently makeing a way for your entire family to have their spiritual needs met? That might require switching churches.
I am sure that if you pray about it, God will give you direction to which body of believers he want's you to be a part of -to serve and to be served (such as child care for your little one).
As far as the noisy little active one goes. I can relate. I too look at what I call, "the library moms" in envy, who have these quiet children who stick shyly by their side and just hug on them and snuggle so calmly only peeking at the rest of us. I don't know how they do it to train them that way. My children want to clap hands, pull at my jewelry, say "PRETTY!" really loud, fuss & shriek when they want to go down and run a muck. And my children are runners with no boundaries. Once they get going with happy little smiles on their faces - the energy takes over and they don't hear me say (yell) "stop". So a small, dark, "cry" room, that has other new mothers nursing sleepy babies doesn't cut it for my children also.
Children have spiritual needs also. They need to be taught about God and His word in creative ways, at their level, in a way that they understand. It's a great idea to get them started with this in the church right from the start so that they grow up being comfortable in the church, away from mom and dad for a while so that they get get fed some bible teachings, and practice a life time habit of participating as a part of the body of Christ. -Even if their participation is to just play and talk with the sweet child care ladies & grandmas for a while.
Your commitment is admirable. With His direction, you'll find a way.