Once you decide which resort you'd like to stay in (I'd choose the Polynesian or the WL- both have a very comfortable and relaxed ambience, and fun pools that will appeal to your youngsters), book the rooms. When you book, have them note right on your reservations that you'd like the rooms close together if possible.
It seems that making this request part of the reservation itself will make it easier for the staff to notice and help with your special requests.
Calling the resort the morning of the day you'll be checking in sounds like a good suggestion, too.
You asked about room size... the Polynesian and the Contemporary rooms sleep 5: two queens and a daybed. The Wilderness Lodge rooms are built for 4: two queens, one queen plus a bunkbed- no daybed.
As far as upgrades go, what is it that you're hoping for? Upgrades are relatively rare, except for the occasional "a slightly better view" upgrade. The odds of getting an upgrade with multiple rooms is even more remote. Book the type/level/view that you really want.
Since you'll be traveling in September, rather than the summer vacation peak, I think your odds of getting rooms pretty near each other is good... you're going to have a fun trip!