I have many options for onsite
These are my first options (If I can find a deal for $220 or less per night, or if I can get
free dining):
1. polynesian
2. fort wilderness lodge
3. animal kingdom lodge
4. contemporary resort
5. grand floridian
6. beach club
7. yacht club
8. boardwalk
If not: split the vacation up between art of animation and a deluxe resort.
If I need a value:
1. art of animation
2. pop century
3. all star movies
4. all star music
5. all star sports
I really don't want to stay at a moderate, because I herd that they have very little kid appeal, and aren't really that exciting.
Oh, I think you may want to check some of them out. I don't remember the ages of your kids, but my DGD is 11. Her favorite resort, bar none, is POFQ. She loves it there so much she asked if we could bring her Pa there last trip. We were staying at the Beach Club and for her, it was not that great.
CBR is also a nice resort. I loved it, my DD and DSIL not so much. It is large, but if you get a preferred room, you are in the center of everything. The pool is pretty awesome!
AKL is my personal favorite. It is gorgeous, has a lot for kids, has a zero entry pool, and animals.
For kids, I think that the GF may not be as much fun, but that is my own opinion. It is kind of stuffy, but you know that everyone is different.
It is pretty hard to say don't take a free offer, and pay to stay onsite, but I can share my own experience when we took Kady for the first time. My first husbands sister was coming with us and she had a very strong opinion to stay offsite to save money. My DD and DSIL were totally opposed and we supported their decision to stay at AKL. Yes, we could have saved money, but the entire experience of being immersed in Disney was worth every penny. We never had to drive anywhere, never had to reenter the "real" world for the entire time we were there. Kady was so enchanted, she wanted to live there
I think that you have an opportunity to compromise, if you don't want to use your entire budget on lodging, step away from the deluxe resorts and price the moderates. I am not saying to stay away from Values, but I have not stayed in any so I cannot give an opinion. I just think that you may want to do a little more research in regards to resort options before ruling anything out.
Anyway, since you are leaning towards a once in a lifetime kind of trip for your kids, I would leans towards onsite. No matter how much your hosts will say that you should do whatever you want to do, you may feel that you must share your time with them. Not saying this is bad, but there is something very special about Disney, and your options are more open if you do not need to consider anyone but your family. After that first big family trip to WDW with Kady, there was a major mutiny in my family. If sis il came, no one would go. Not one of my family would vacation with her again, and even though she was very accommodating during the entire trip, she really got on everyone's nerves. I had to plan an extra trip because she was so upset. We learned out lesson.