I know that alot of people just buy extra luggage when the are here. The "Disney" Wal-mart located on Turkey Lake road has like 2 aisle of luggage ( we call it that as it has so much Disney stuff and touristy stuff in it) You might think about going this route, so you get a bag that is the right size, just a suggestion.
You also could do like a Vera Bradley weekender or a large tote, and make that your personal carry on...or they will fold up to put into the luggage, for the kids use bigger backpacks, Bring enough so everyone can help distribute the loot...I use my Vera Bradley weekender as my handbag and it fits under the seat perfect. On a side note make sure that you put your real purse in it before boarding... so leave room. I use a small crossbody so it fits easily into the bigger bag... DH has 2 travel backpacks... one we use on easy day trips its smaller, but if we are going to be on a all day tour, or riding a bus for a couple of hours each way, we pull out the bigger one that can hold alot more stuff, i-pad, jackets, scarves, gloves, snacks, bottle water and anything that we might buy. So normally the big one gets packed in the luggage and used as we need it.