Hello, if this is the company
http://www.sunshineorlandorentals.com/ I looked at the web site and they have lots of homes in lots of locations that range from pretty close to Disney (Emerald Island (where we owned several years ago), Windsor Hills, Sunset Lakes (where we live 3 months), and Lindfields. There are many other homes that are in locations that are sorta close to Disney to really quite a ways out.
Website is nicely done and frankly the number of homes is pretty impressive. They have obviously recruited many private owners to put their home on this site. Probably the vast majority of these homes are privately owned and with a little research could be found on other company websites as well as on "by owner" sites.
I did notice they did not let you link to the "owner's website" the home would probably rent if for less if you go directly through the owner, and the rental company is not taking a commission.
One thing that stood out to me is no 800 or toll free number. The number is 407 which is Disney area code and you pay for the call. This is little cheap if you ask me! With a little searching I did find this under contact us...Toll Free: 1-866-849-2434.
So, looks to me like they have a nice selection of homes and are probably a newer company as I have not heard of them either. They did come up on first page of Google when I searched Sunshine rentals orlando.
That is best I can do based on what I see on the this site...
Ted