At my wedding, my now ex-wife insisted on no kids. My sister in law and mother were not happy that my 1 yr old nephew was not allowed. We arranged day care in a side room of the church. They said he would be fine, but I didn't give in. When they arrived in town they related how he cried the whole time on the flights. That ended the discussion. A crying baby at a wedding can ruin the event, especially for the bride. And if a baby starts crying, one of the parents will have to take it about of the church, so now you have an adult missing the ceremony. How is that better than very young children missing it?
OP, you need to get over it. Yes, you are paying for the wedding. No, you don't have much say in the details unless it is extravagant things that take it way over budget. That's how it is. It's the bride's day. You are just going to alienate her and your wife. If you can find a room in the church for the kids they can be retrieved for pictures, but make it just one or two so the picture process doesn't grind to a halt waiting for the kids to pose acceptably.