Definitely lots of immodium. We went in July of one year and the wait in line for Splash Mountain was right at two hours. Other popular rides were about an hour to an hour and a half. There was usually no waiting at the educational "rides" in the Future section. If you're going to see Mickey, wait to do it late in the day. They used to have him at his house all day long, but if you go at night, when the crowds are getting thinned out, you don't have such a wait. I was like third in line because we waited until well after dark. My mother and I also found that the fireworks display (I don't know if they still do that) was a great time to ride rides as everyone was busy watching the fireworks.
Even if you don't feel up to standing in line for two hours for a ride, you can always trade up kids with your husband. Let him take one (or more) and go do the waiting-in-line thing for rides, while you take another one (or more) and ride around the park on the train and go see the shows and educational bits that don't require you to be stuck in one place for a long time, and then you guys can met up somewhere for lunch and trade out kids; he can take your set on the rides and you can take his set to the shows. Then if it does thin out in the evening, you can take a shot at going on some rides too. The kids will enjoy having some quality mom or dad time away from their sibilings too and both of you should be less stressed since you'll deal with less kids at one time. Epcot, on the other hand, doesn't require much waiting in line, so you can all do that together.
Oh, and they do have first aid stations around the parks if you need to go somewhere cool, get some water, take some more immodium, have a sit, etc. My mother got sick at Epcot on our second trip down there (we suspect food poisioning from her turkey sandwich the day before at Disney World--avoid turkey sandwiches!)
Don't go to MGM. That was so disappointing; there was hardly anything there to see; while my mother and I stayed at Disney World until they closed it at midnight or 1 am, we left MGM at about 2 in the afternoon. We wished we had spent the day at a waterpark instead. They didn't have the Wild Kingdom park when I was there, but I've heard good things. You might want to check and see how long you are on the bus or jeep or whatever, though, just in case it's a long time until a pit stop.
That's great news about your nephew. I used to watch some of the St. Jude's specials on tv; it's so sad that children so young have to be so sick and bear such a burden. You might find this trip a good time to spend some quality aunt time with him, since he may not have the energy that your healthy children have. You two can be sick buddies together. Commiserating with someone else who understands what it's like to be sick or to hurt all the time makes you feel not so bad. Haven't figured out why, but it does. Plus you don't feel so left out and don't feel like you're dragging everyone else down too when you have someone else who can't do as much. You probably can make each other feel better.
Also, check online and/or in some of the guide books made just for the park; I have heard that Disney will do special things for sick and handicapped children, like setting up a personal meeting with Mickey, souviners, even letting some handicapped or very sick children get their own tour guide who bumps them to the head of the line at rides since they are too sick to wait it out. So see if they will arrange anything special for your nephew; what a treat that would be!