We had our first trip in May with our 2, 4, and 9yo. We were not concerned with "doing it all" and really wanted to relax and enjoy our time. We did not do the dining plan and didn't make any ADRs because we didn't want to worry about being in a certain park at a certain time. If the kids got cranky or sick I didn't want to feel obligated to stay in a park until our dinner time rolled around. I had a schedule of park/EMH hours and we had some idea of which parks we wanted to do which days and tried to alternate sleeping in and getting to EMHs, but we left it flexible enough that we could change our mind the night before (or when DS threw up at the bus stop heading to Epcot

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The schedule that we wound up doing most days was: go to a park in the morning until about 11-12, head back to the room and nap, go back to another park from about 5-8:30. I was a little wary of the napping. My two older kids do not take naps and I didn't know if the youngest would with everyone there. We closed the curtains and all layed down. Almost every time we ALL fell asleep for up to 4 hours. (Once DD9 and I walked around the resort and got ice cream because we didnt fall asleep with everyone else.) It kept us from getting over-tired in the parks and also got us out of the heat in the afternoon. Also leaving the parks by about 8:30 got us out before the crowd and we were able to get back to the room, snack, bathe, and be in bed before 10. We were usually only in a park for 3-4 hours at a time, so the kids never got overstimulated or exhausted which amazingly meant no meltdowns for us.
One thing I would not miss with little ones is am EMH at MK. We did this 3 times during our trip and were able to do everything in Fantasyland basically walk-on. We then did a few other areas of the park until the lines started to form (usually around 11:00). We got more done in those 3 hours than I think we would have if we stayed the whole rest of the day. A few times we were in MK in the afternoon/evening some of the wait times for things like Peter Pan were 70-90 minutes.
We had food in our room and brought alot of snacks into the parks. We also used hydration backpacks, so we always had water to drink. This made it very nice when the kids got hungry or thirsty standing in line or moving through the parks.
If your 4 year old is tall enough for the height restricted rides, make sure you use the rider switch passes and/or fastpass so one parent won't be stuck waiting with the little one forever.
Make sure you have two strollers or rent a double. My kids have never used strollers (we bought them just for Disney), but they stayed in them whenever we were walking around the parks. They didn't get tired/hot and it was really nice to not have to worry about them getting run over/lost in the crowds. I met several people who thought they would just need a stroller for their baby, but wound up carrying the baby while the older child needed to sit.
You will have a great trip.
