With a crew of those ages, I would definitely stay offsite. Yeah, Disney gives you transportation and a heaping dose of pixie dust, but comfort is key. If I couldn't rent points from a member, I would be looking to stay offsite and rent a car. You're going to spend some dough at the moderates and that could be applied to having more comfort in your hotel stay. This, however, is coming from someone who doesn't look at a hotel room as simply a place to "sleep and shower."
Depending on when you go, you can get some decent car rental deals and staying somewhere like
The Fountains or
WorldQuest would be ideal for you.
Where it gets tricky on your budget is with admission media. I would probably choose two Disney parks and one Universal to accommodate everyone. The teens will love Universal (stick with Islands, here) and the younger ones will have a great time at Disney. I have a Universal AP and some non-expiration hoppers in reserve (I try to buy before the annual rate hike), but my employer also has discounted tickets available. The discounts aren't huge (think ten to fifteen percent) but there was a reasonably priced Disney/Universal combo from our employer that I got one year. We had multiple park tastes to consider and that turned out to be the best thing for us then. Check that avenue; sometimes companies have negotiated tickets that aren't available for purchase elsewhere.
I agree that first, you need to set a budget and determine the time of year you'd like to go. Secondly, I would make some hard decisions to decide WHERE to go. You know your family best; if they'd like non-stop, commando-style touring, then try to fit as much in as possible. If you think they'd benefit from having breaks, then schedule less. I believe it's possible to do "everything" at Disney/Universal, but I also know I'm never going to try. God willing, there'll always be a next time.
Happy planning!
