My ex and I weren't walking with God while married, and both are now. I have been going to the same church for 3 years. Ex is moving on to church #3 (and soon, wife #4). Yes, they know they have two homes, and two churches. I like to joke that my kids are bichurchal!!!
From your post it appears that your kids would continue to go to that church on dads weekend, which is good. Nothing wrong with bringing them to a new church if you decide to find another one either. I am with everyone else on this. Pray about it. But if you feel you are not getting fed at your church, maybe it is time to look around.
Beth