I am a single mom of one so I cannot really speak to how the rooms work for a family your size. But like the pp said there are options. We have stayed at All Star Sports, CSR, and CBR. As far as rooms go, the size seems about the same. But the moderate rooms do measure a little larger. Also, I have heard that many people take advantage of the trundle beds at POR. I like the extra room for changing behind the curtain at the moderates, and I like having the fridge in the room at the moderates. But we make do very well without these when in the values.
The theming is great in all the Disney resorts. I really think the kids will have a great time in any resort you choose.
Sounds like money is an issue. Be sure to keep checking for deals and codes. I hope you have found mousesavers and mousemisers by now. Both are great resources. We will be staying at POFQ in August for $89/night with an AP rate.
Being a single parent has it's challenges. Financially speaking I find that I can take my son to Disney for about what I spend anywhere else we vacation. Plus, at Disney I can really relax and know that we are safe and that there will always be something for us to enjoy. Beyond the themeparks there are tons of water activities (from swimming to watercraft rental), Downtown Disney, the Boardwalk, mini golf, Campfire and a Movie at Fort Wilderness (movies are also shown at several other resorts now including All Star Music), ..... I could go on and on!
Good luck in saving for your trip. Don't give up on your goal and have a great time with your kids.