Which of the options is the best for your group does depend a little on the ages and make up of the group. With 4 small children (all under 10 years) then the hotel suites should be more than enough room. If the kids are a little older/large and it would be difficult/embarrassing to have them share beds then it may be better to go for the largest unit type (a vacation home). Personally I'd go for the vacation home if you have your own car (or hire one). It will give you at least 2 bathrooms for the group, all the kids will get their own bed and bedroom, the adults can send the kids to bed and stay up a little later, enjoying a glass of wine,a beer and each other's company. You can also save a lot of money on food and drink costs, even if that just means having cereal, toast and bagels for breakfast and taking a couple of sodas each with you into the parks.
If you want hotel like facilities (communal pools etc) then there are a large number of suite hotels that would cover your needs. One of the best ways to get a deal on these is on
http://www.hotwire.com , you don't know the actual resort until after you commit, but if you keep checking the website you will often find a great deal pops up from time to time.
Timeshare resorts are another option and many of those will offer a very good deal for your room costs ( for a short stay) if you agree to take their timeshare sales pitch. It does mean you have to give up a morning to go through the sales pitch, but for a 3 or 4 night stay it probably is the best way to get top class accommodation for the lowest cost. You will often see 3 or 4 night stays in a 2 bedroom unit ( up to 8 people) on offer for a total cost of $200-250.
With that group size, if you have your own transport I think a vacation home offers the most spacious accommodation at the best cost. Using a reputable local management company is one option, it does mean you pay slightly more for the house, but does give you some extra safeguards.
http://www.pr-vacation.com is a company I have dealt with a lot in the past and was always happy with them. If you rent direct from the owner it can save you a little extra money
http://www.vrbo.com is a good place to get a lot of information on the options this style of vacation choice can give you.