Hi, Jessie! Last week, I took an in-depth look into the baby care center at the MK, and it provides a great place for parents and babies to take a break from the weather and the crowds to rest and replenish their energy. The center has a kitchen to make/heat bottles or food, a place to buy supplies, rooms to change a diaper or clothes, and a place for older siblings to sit, watch TV or draw a picture. There are even quiet, semi-dark rooms for nursing mothers.
If a baby center is going to be closed for a period of time, they are usually located near the First Aid area which would make a great alternative for a baby care center in case you need a place to nurse or cool down. Just remember that they are not equipped (like the baby care center) to take care of the entire family. So, you may need to ask Dad and any others to wait at an alternative location. Both locations require that you park strollers outside their facilities. In addition, each park's restrooms are equipped with baby changing areas, and inside attractions are great places for quick naps or cool down spots. Table service restaurants (without characters) are also good places to take a break from the weather and the crowds. I hope this has helped alleviate any concerns. Have a wonderful day and a magical vacation!