Hi Debra!
Your daughter will have such a wonderful time celebrating her 8th Birthday with her family and grandmothers at Walt Disney World!
In terms of cost-effectiveness and privacy for the adults in your party, my top recommendation would be for you to consider reserving 2 adjoining and connected rooms at a Moderate level resort. You'll actually have more space and privacy in this set up than you would in a studio or 1-bedroom suite. You can choose to keep the interior, adjoining door open to have the feel of staying 'together' without compromising or having any adults in your party needing to sleep on pull out sofas or sleeper chairs. Since it's your daughter's birthday, consider the new Princess-themed
Royal Rooms at Disney's Port Orleans Riverside Resort. In the fall season, this room type is approximately $200/night/room and provides 2 queen-size beds per room.
Villa studio or suite accommodations would provide a separate bedroom with queen or king size bed along with pull-out sofa(s) and/or sleeper chairs. Pricing on these room types begin at a little more than $300/night with 2-bedroom suites beginning in the $600's. It really depends on whether your moms would be comfortable sleeping in the same bed or on a pull-out! I recommend you visit the links here to peruse the possible set-ups that would best suit your needs.
Once you've taken a bit of a look, please feel free to visit me again if I can provide any further assistance or answer more of your questions to help you make the best decision for your vacation.
Wishing you a simply Magical time on your daughter's Birthday Trip to Walt Disney World Debra!
Kirsten