Rachael, you don't break down the exact make up of your group, but I'm guessing there are more than one family/set of adults.
What could be a workable idea for your group, one that cuts down on having to pack up ALL your stuff to move it around, that would give all of you a break from each other as well as the parks would be to keep your villa in the WDW area for the whole 3 weeks and each family/set of adults take a short (2,3 or 4 nights) break at different times to different places. That way it gives you more coverage of areas (maybe ideas for a future trip), it allows you to just pack a bag for a few days, gives the group a break from each other just in case things are getting a little too claustrophobic. For example if you all arrived in Fl on day 1, stayed together for 5 days, then on day 6 family/group one went to Captiva/Naples for 3 days/nights. day 10-14 spend together in the parks, days 15-17 family/group two go to St Augustine/Miami/Vero beach and then join up for the last 3/4 days together. IMHO no matter how well families/friends/kids get on at home, being on vacation together in the same villa can become a little wearing after 3 weeks. Usually over the smallest things, building in enforced breaks allows any friction to cool and also gives you something different to talk about when the groups get back together again.
Even if it's mom,dad 3 kids and one set of grandparents, this can work well if mom and dad (maybe one smaller kid if necessary) go off alone to the beach for a couple of days and later the grand parents take a few days out on their own to recover from the demands of having grand kids around 24/7.
Doesn't work for everyone, but IMHO it's worth considering. The logistics of packing up EVERYONE then moving camp can be quite tiring and take up valuable vacation time, throwing a few clothes in a suitcase and heading off is a much less traumatic and time consuming experience. Letting mom and dad have a little time to themselves is a rare pleasure from most parents and even just a couple of days quality time together can make a family holiday a special experience for the (usually rushed/stressed) parents as well.