What is a medical child support order?

My kids’ mother has filed a child support action against me and in it she’s asking that the court issue a ‘medical support order’ and make me provide health insurance for my kids on top of child support. Insurance at my company is extremely expensive and if I carry my kids on the plan there is no way I can pay child support also. I think it makes more sense for her to cover the kids on her insurance, it’s cheaper. What exactly is a medical support order and can I fight it? If I am required to provide health insurance for the kids, could a judge waive child support? Also, how do I respond to her court papers? The paperwork says I have a certain amount of days to respond but is that from when she filed the papers or when I received them?