Putting the money issues aside...
I can tell you with kids, you'll fall in love with using a timeshare. We are spoiled by them now.
- No more sitting in hotel bathroom waiting on the kids to go to sleep in the hotel room.
- No more begging everyone to get up and shower and getting dressed just to eat breakfast.
- No more arguments over which tv show to watch
- Think of all the savings of going to the grocery store and just buying breakfast foods for the week!
- Less packing because you can wash your clothes.
- very simply -- MORE SPACE!

couldn't have said it better myself!! We discovered timesharing a little less than three years ago when we happened to win a week at Ko'Olina at a fundraiser auction at my daughter's law school. At the time, our daughters were already out of the house and we had traveled fairly extensively with the kids and my parents over the previous 15 years or so, often with the girls sharing a room with us (DH loved sharing a bathroom with 3 girls

) and the morning cry that started the day- where to go for breakfast

. After two days at Ko'Olina my hubbie turned and said to me: "wht would you ever want to travel any other way?!"
Unfortunately, I was ignorant as to how nice timeshares could be, and just knew about the kinda ratty cabin-type places of yester-year. With three young kids especially you won't regret your decision to buy.
HOWEVER, that said, RESCIND IMMEDIATELY and take your time to read, ask lots of questions and then decide if you want to buy directly and have the ability to trade for points or save $$$'s up front and buy resale. You'll have the time to consider whether Horizons is the right place to buy, away from the vacation-high, so to speak. As pointed out above, the opportunity will be there in a month or a few months down the road, but once you've committed, you may regret your decision and you'll be stuck.
Read several months of posts here, ask questions as they come up, and then decide. The best advice I can give you now is rescind immediately and then put this aside and enjoy the rest of your trip. When you get home you can stay up at night and research to your heart's content.
Welcome to Tug, btw

- and congrats on finding the Board before being stuck in something that you may very well regret.