First, welcome to DR1!
You've gotten some very good advice thus far, some of it from folks who were in your shoes not too long ago.
My advice would be: take a deep breath, and slow down.
Lots of people are super excited when they decide to move someplace new, but as this decision will affect your entire family, it's best to consider a few things:
Do you really want to move there? I mean, DR in particular, vs. some general spot in the caribbean? The only way to make sure is to travel there and stay for a while. And NOT as a tourist, rent a apartment and stay put for, say, the summer. DR is great, but you should go into any major life choice with your eyes wide open.
Residency is something you should start discussing with your local consulate AFTER you've spent time in-country, and have made the decision.
There are many places to choose from in DR, ranging from ultra-touristy to never seeing another gringo again. The cost of living is frequently directly proportionate to the emphasis the area places on tourism.
Keep in mind that purchasing real estate is almost laughably easy. Selling it is an altogether different matter.
You've got one kid in high school, another knocking on the door. The public schools are pretty poor across the board, although many areas have at least one decent private school. While a fraction of the cost of NA, you're still looking at $1,000 per month, per student.
A suggestion: as you've got a kid who has almost graduated high school, consider spending the next few summers in DR. Try a few different areas (Santo Domingo, Punta Cana, La Romana, Las Terrenas, Santiago, Cabrera and Cabarete/Sosua are all great options), and take it all in. In two years, your oldest will have graduated, which will save oodles of money, and you'll hopefully know the area and language well enough to make some realistic decisions.
So take your time, learn the country, and gradually ease in. Best of luck!