Which resort, what size and in what type of building are you getting the Westgate room? There is a BIG difference. We stayed at the Wesgate Lakes Resort in May of last year. The resort was nice, but the the rooms range from very extravagant to very old. Clean, but old. We were there on a rental, NOT on their Time Share preview package. We had an older 1BR unit, which was large but definitely showed a lot of signs of its' age. The on-site pools, putt-putt, activities for the kids, etc. were great. We were so impressed with the resort initially (not the people or service), that after a couple of days, we prepaid for our next vacation (no we didn't buy a timeshare, we went ahead and prepaid for a future week of vacation - difference is no dues/fees or long term commitments). Needless to say, the service was so bad on the last couple of days, we got a refund for that prepay before we left Orlando. At this particular Westgate property, service is NOT a strong suit.
With 3 kids, if you can get a newer building, 1BR or larger unit, and it is still $800 less, then I would say yes, definitely worth entertaining. For an older unit, or an efficiency, I would spend the extra dough at AoA.