The religious ping-pong — I can only speak on my experiences and give my opinion about what worked for me, so if it matches what you are going through, great!
My father is Catholic and my mother is born-again Christian. When my parents married my dad got baptized and became born-again. We practiced born-again Christianity every Sunday like a good little family should. When my parents divorced, my father actually didn't go to church for a while until he met his new wife, who was and is Catholic. So surprise, surprise — my father switched back to Catholicism.
I never worried about which church to go to up until this point because I had been going to the same church my whole life. One weekend my father took me to Catholic Church with him and I was so confused. I didn't understand all the sit, kneel, stand, sign of the cross, sit, stand, kneel, sit, stand, and "also with you" stuff. I gradually learned over time what to do and was fine.
You might say to yourself, "Well they were both Christian; how different could the two churches be?" Well, I went to the Church of Christ, which is the staunchest church you can go to. They don't even have instrumental music because it wasn't ordained in the New Testament. The Catholic Church has huge organs that bellow out sound from all corners of the building. At the Church of Christ there are no statues representing Christ dying on the cross, Saints, or anything else because that is considered idolatry and they also believe that you must be baptized in water and be completely submerged in order to wash away your sins. No sprinkling of water like in the Catholic Church. They also don't believe in baptizing babies because babies have no sin (and trust me, with Catholics that starts a whole new conversation).
My mother later asked me, "So how did you like Catholic Church today?" I replied, "It was short". You see, I was used to going to church and the preacher going on for hours and so would the singing. The Catholic Church lasted for an hour, exactly, and did not stray from that. There was a nice little book that told you when to stand, what to say, and there were no bibles in site except for that of the priest. I found it all a little odd. Not that it was wrong but that it was different from what I was used to.
My mother and father never made me make a choice in what church I wanted to attend. Whoever I was with that weekend, I just attended their church. It was no big deal. I'm guessing it would have been harder had one parent been Muslim and the other Jewish. There would have been a war or something over where to go. But since my parents were both Christian, I was fine. Of course, both churches preached that they were the one TRUE church and that following any other church would be wrong — but I took that with a grain of salt.
What do I practice now, you may ask? Well, I'm still Christian but I now attend the United Unitarian Church. All are welcome there. I believe that there is no one way to get into heaven. Do I believe in Jesus, yes! But I believe God knows our hearts and as long as we are good people doing good works in this life we will enter the kingdom of heaven. I took what I learned from not only my parent's churches, but also my friend's synagogues, temples, and mosques. I looked into all the religions a little and found that the one thing they all say is to treat people the way you want to be treated. So I do that daily.
Ultimately, in opinion, I think religion is something you should show your child to give them a good moral fiber, but in the end they need to have a passion for whatever religion they follow or else they are simply doing to it for you and not for themselves. Religion should truly be in your very being and should never be forced upon someone; otherwise it goes against all the teaching of that religion.
That's my opinion. Like it or not that is how I think and how I was raised. What is your opinion? How are you people out there that are "unevenly yoked" raising your kids?