More time to pay less monthly support?

My estranged husband and I have been separated for four years now. We have been somewhat amicable on everything as far as support as well as custody. The main reason we split is because he completely ignored and neglected our daughter and continued to do so until about ten months ago when he started to date a woman who had two kids. He suddenly wanted to pretend he was a great dad by taking our daughter every other weekend which I agreed to. I recently told him we needed to modify our child support agreement because of healthcare costs as well as I now have to pay for before and after school childcare as I didn’t need to before because my mother watched her but has now gone back to work. He now wants our daughter not only every other Friday and Saturday night but now every other Friday, Saturday, Sunday, Monday and Tuesday night. I know he only wants her more days to avoid paying more child support because he has neglected her most of her life, also when she does visit him at his two bedroom apartment which he shares with his girlfriend and her two girls, my daughter has to sleep on a mattress on the floor while the other girls have their own beds. I don’t feel like it’s a stable situation for her. What can I do and if we bump heads on this could he take me to court and get her every other week?

He could file an action seeking 50% custody. Based on the current custodial arrangement and his past attitude towards your daughter I believe he would have an uphill battle, especially considering the environment he provides.