going offsite without a car is not a good ideal.
if you must stay offsite then go with WDW and forget the other parks for this trip.
especially with a large family - so if someone get sicks - you don't all have to leave.
even the best offsite transportation only goes a couple of times in the morning and take you back in the afternoon - evening. If someone gets sick you will have to get a taxi.
with buy 4 - get 3 free - might go for 2 value rooms.
that say if you insist
Sheraton Vistana Resort
Marriott's Grande Vista
Wynham Bonnett Creek
but check before you made the reservation - they definitely provide transporation (for a cost - a rental car will be cheaper) to WDW - but some have cut back - economy to the other parks