If I get medically retired, can I stay in my on-post house and are my kids still allowed to go to their school and daycare?

No you cannot. Unless your post is one that allows civilians, and your housing area is one of the housing areas selected for that, when you retire you have to leave.

In the past it would have been an outright no but in recent years certain OnBase housing have transitioned to allow retirees. It is not guaranteed as not all Bases and housing management groups allow it but it is a thing and in most areas it is a limited service to specific housing. You will need to check with local housing to see what your options are. You will also need to speak to them about all the angles as being medically retired under DOD retirement time in service creates a few potential gaps. Hope this helps.

https://www.military.com/money/home-ownership/renting-house/retirees-civilians-want-live-base-housing-yes-you-can.html

SSG (Join to see) From my understanding is that you will receive your orders for medical discharge. At that point you will have to do like everyone else and clear housing, base etc, just like PSCing. I would get with the housing office and discuss with them on what your options are.