My two children are 7 & 10 also. They're used to going to bed early, though, and waking up early. Unfortunately, even if they go to bed late they still wake up early, so I'd be dragging two bears through the parks. We find that at least every second night at WDW we have to get them to bed close to their usual time of 8:30. They're generally awake at 6:00 or 6:30 a.m., though, so we're always up bright and early for EE.
If your boys are used to staying up later - go for it! If not, you might want to let them sleep in a bit the next morning so they'll be rested for a busy day.
If you show up a bit early for your PS, at 7:00 or so, you should be finished by 8:30 (assuming a reasonable wait time) and then you can zip around the resort loop on the monorail and still drive back to POR and get them in bed by 9:30 or 10:00 at the latest.
Don't forget to ask the monorail attendant if it would be possible to sit in the front of the monorail with the driver. It depends on whether another family is there before you, but that provides a wonderful first view of WDW. However, you'll only see a bit of the Magic Kingdom if you travel around the resort loop. You could transfer to the Epcot monorail, which provides a quick view of the very front of Epcot, but I'm guessing that would add at least another 30 minutes to your tour. AK and MGM are not serviced by the monorail.
Have a blast!