We had never taken a mid-day break before, but when I planned our first summer trip last year (end of Aug.) I built a break into pretty much every day due to the heat. Kids were 12 & 8. I assumed we'd all need it but knew I wouldn't be thrilled taking a break. Also assumed the kids would want to swim most days.
The first day they did swim; after that, we did just what the OP is thinking may happen to her family - got to the room and said, "now what?" Kids would ask how long we were staying in the room and DH would pace back and forth lol. Nobody wanted to/can nap during the day. Since we have a pool at home and older DS isn't big on swimming anyway, the appeal just wasn't there. So, it ended up the rest of the vacation we either a. went to the parks late morning, had a TS lunch and stayed late, b. left park and had TS lunch at a resort, toured resort for awhile for a "break", maybe went to our resort to shower/change QUICK and back to park, or c. went to park late morning, stopped at resort late afternoon QUICK to shower/change. I have to stress the word QUICK here b/c overall we didn't want to break, but our disgusting sweaty clothes won out

It may seem that given the time it takes to get back to the resort, only staying there an hour, hour and a half is pointless, but if refreshed us and got us back to the park which is where we wanted to be

Missing RD didn't matter to us on that trip: crowds weren't heavy, and it was ridiculously hot regardless of what time it was.
Should we visit again in the hot months I'll most likely plan on us going to the parks later in the day and staying till close, or breaking for a TS lunch at a resort for our "park break". Different strokes for different folks!