Transportation recommendations...
To the Theme Parks - Of most interest is the shuttle bus.  There is a third-party shuttle service from the Windsor resorts to the themeparks called MainGate shuttle service (www.maingatetaxi.com).  They charge $10 per person per day per round trip to the parks.  Based solely on cost, we don't recommend this option.  Depending on the size of your party, that goes a long way to paying for a rental car.
As an alternative option, consider taking a taxi from the resort to Animal Kingdom lodge (2 miles away) for $8 for up to five people and inject the yourselves into complimentary Disney transportation (buses) to anywhere in WDW.  It is less expensive and you leave when you want.
Area Transportation - When visiting Orlando, the distances are spread out enough and the public transportation inconvenient enough (even Disney transportation) that we really recommend that you rent a car.  When you are paying $75+ per day for admission to a theme park and your family is exhausted when you exit a theme park, the cost of the delays and toll on your energy make public transportation more expensive than first calculated.
A trip to & from Orlando International Airport from our homes or the Disney area takes about 25 minutes by car and is relatively easy & direct.  The path only hits four major roads with well marked turns.  A taxi from the airport to the Disney area costs $50 to $60, so the cost of a round trip goes a long way towards paying for a rental car.  There is a city bus that takes you from the airport to several spots where you can connect with Disney transportation (another bus) for about $3 per person, but it takes about an hour & 15 minutes and you have to juggle your luggage.  You can get as close as Animal Kingdom Lodge, but still have to get a taxi from that point.
Travel sites like www.travelocity.com or www.expedia.com are always running specials on rental cars that actually make them less expensive than taxis without the incredible delays of other public transportation.  Except for the theme parks, parking is usually free.  Admittedly, parking at the theme parks is expensive (currently $14 per day at Disney), but you pay it only once a day, and only for the days you visit major theme park.  Travel time to & from your vacation home is only 5 to 10 minutes and you can come and go as you wish with minimal delays.  We actually recommend that you come back to your home for lunch & a nap to get the most out of Disney.
Orlando has so much to offer than just Disney.  Without a car you are almost as limited as those who are staying in the Disney resorts:  only Disney parks & only Disney restaurants and there is so much more to Orlando.  There is Universal Studios, Islands of Adventure, SeaWorld, Aquatica, Kennedy Space Center, Discovery Cove, Busch Gardens, and literally hundreds of minor attractions that cease to be an option without a car.
If your group is renting a car, but is splitting up, or is too big to fit in a single vehicle, the five minute drive to shuttle part of your group to either the desired theme park or the Animal Kingdom Lodge is still an option to consider.