Hi Maggie!
It can be overwhelming, I went through the process myself a few months ago for our upcoming trip in November.
Here's my advice:
1. I'd decide on a budget.
What is the max you are willing to spend per night? (Include tax, and pool heat if you are traveling from Nov - Apr). Prices vary according to your travel dates. Christmas, Thanksgiving, and Spring Break weeks are pricey everywhere. Depending on the time of year and your neighborhood, you can expect to spend as little as $600 or as much as $2k for a week for a 3-4 bedroom home pool home.
2. Decide what amenities you want.
I personally would suggest a home with private pool, that way you don't have hike to the pool to keep an eye on your boys while they are swimming. Also, I'd think the games room would be ideal for your boys... I'm sure they'd enjoy playing pool, air hockey, or foosball. Many of the homes have high end video games players that the older kids like. Do you want a private pool, as well as a main resort pool / community complex? (that will narrow your neighborhood choices too)
3. Determine an geographic area that you want to be in.
Here's a map that shows many of the developments:
http://www.thedibb.co.uk/villa/map.htm
The Formosa Gardens area of Kissimee is generally the closest to WDW. There are lots of developments in this area includes Windsor Hills.
If you really want a pool home, but want to spend a little less money, look out in the Davenport area. (Generally you can get a pool home in this area for about the same money as a town home in the Formosa Gardens area.) There are lots of developments in/around the Champions Gate area of Davenport that have nice homes. These homes rent for less, partly because of the longer distance to WDW. You'll spend an extra 10-12 minutes traveling back and forth then if you stayed in the Formosa Gardens area. But it might be nice of everyone to have their own bedroom and bathroom.
Here's a recent thread that talks about Westhaven area out in Davenport.
http://www.disboards.com/showthread.php?t=1487605
One person included a link to a home that they recently rented, and it looks very nice, for $750 - $970 per week including tax.
4. Focus in on a few neighborhoods, and start scrolling down the list on one of the rental websites.
Once you decide on a geographic area, or a few neighborhoods, you can always post again and ask for specific suggestions.
btw, the vast majority of homes are pet free... I bet more than 97% are pet free homes... so no worries there.
Good luck searching!
Lisa