Welcome! You will all have a great time at WDW. There's something for everyone. Well, renting a car is really a personal decision. I ususally stay on-site, but still like to have a car for side trips to the grocery store, etc. If I was staying off-site, I would most certainly want a car because I don't like to have to wait for a crowded bus back to my hotel after a long day at the parks. I'd check with your hotel though on their bus service.
As far as your DSs, there are lots of good rides at MK and your DD can see her Princesses too. Most of the rides at WDW are fairly tame. No major coasters, so you all can probably go on the rides depending on DD's height (and is she is agreeable).
I suggest going to MGM and MK for the rides and characters. I personally love EPCOT, but can see that it might not be the best one for teens. As far as AK, it's a nice park and they do have some good rides for your DS's.
As far as tix go, I like the park hoppers, but I'm not sure about 3 day park hoppers. I normally buy the 5 day PH for my DH and DDs. I have an AP for myself for the discounts. I like the 5 days because I know we will always come back to WDW and these are good for life. Prices are always going up, so you are ultimately saving money if you plan on coming back.
Hope I could answer some of your questions. Enjoy your trip!
