Never heard of prebooking seats or how you would do this - we have just turned up early especially for the ice show and one night at the karaoke.
I too am unaware of any seat booking system on Independence, they, in fact, point out there is no "keeping seats" allowed. If you are early (main) dining you will be finished about 7.30-7.45 for the main show at 9.00pm. Theatre opens about 8.15-8.30 which should give you time to get there and get a seat. If you are late dining then the main show is usually before you eat, again get there early and you shouldn't have difficulty getting a seat. Ice rink opens 30 minutes before the show, similar advice applies.
There was never a problem getting seats as long as you turn up at least 15 minutes before a performance. The Theatre had ample capacity.
I agree with the others but I have a view that if you don't ask you won't get so go to guest services and see what might be done. There are spaces for wheelchairs on the theatre plan on the ship so that might the answer, borrow a wheelchair for evening use. In my vocabularly there is no such word is it can't be done, worth a try or think of something else along the lines of my suggestion. If you do book an excursion ask if the reserve seats at the front of the bus for you, if they don't ask why not.