We first went to Disney World when our autistic son was about 5 or 6, and our main strategies were:
1. stroller-as-wheelchair for many of the reasons listed above
2. avoidance of lines to the greatest extent possible due to sensory issues (combination of FP+ and
DAS now seem to work pretty well for this)
3. many breaks
Everything went really well. There were a few occasions when my son and I (or my wife) would head back to the hotel earlier than planned, but that was easy.
For breaks, we would:
1. Sprinkle in various shows throughout the day: we got to relax for a while (oftentimes in air conditioning) before the show started, and some of the shows have fairly open floor plans for stimming/pacing/flapping, if needed
2. Go back to the hotel during the middle of the day for a 2-3 hour break. I don't know which parks you plan on visiting, but we found that staying at one of the Epcot area resorts (Boardwalk, Yacht Club, Beach Club, Dolphin or Swan resorts) helps with breaks for two of the parks (Epcot and Disney Hollywood Studios) since you can easily walk or take a boat to and from those parks.
3. Take full days off during the week. Again, I don't know how long you are going for, but our rule is never to have more than 2 days in a row at amusement parks. Now, "full day off" doesn't really mean that. We might go to one of the water parks for a few hours, or go hang out in Disney Springs for a couple hours, or even eat in one of the parks for dinner, but no long lines and no amusement rides. The main point is we have a nice, lazy morning and usually an early evening on these days off such that we rest-up.
Plus, time at the hotel (either #2 or #3 above) often meant time at the hotel pool which was a big hit with our son (especially at the Yacht or Beach Club which has the best pool of any of the hotels).
I would definitely think carefully about your worries/concerns/triggers for each son, and on your first morning at Disney, go to Guest Relations at whichever park you go to and succinctly discuss your concerns with them. They are very helpful and will give you their thoughts and/or options to address your concerns (including showing you a map with locations of the family restrooms).
Our son really had a good time. He is now 10, and we are now scheduling our 4th trip there. Each time, we have had less and less to be concerned about, and he always has a good time. BTW, his neurotypical older sister really enjoys these trips as well!