When my ex has contact with our daughter, should I have to supply everything, like push chair car seat

Sorry but I cannot understand your question.
Does your ex have a court ordered visitation?

There is no legal requirement unless its written into your custody order. But why wouldn't you want your child to have familiar things? Sounds to me like you are trying to stick it to the ex at the expense of your child.

when my ex has contact with our daughter, should i have to supply everything, like push chair car seat

I don't think it's required of you to provide a stroller, car seat, etc. but as Scott said, why is it an issue to do so? If you already have the items, why is it an issue to swap back and forth? It seems like much more work and money to buy duplicates of everything.