I'll take my cue from MommC and say, Hello, I'm Hillbilly, a 40 year resident of the DR, who has raised a large-well huge might be a better word-family here.
1) The kids. I would expect that your first answers of Santiago and Santo Domingo could be complimented with others, like La Vega, Moca, Jarabacoa, Mao, since all of them are less than 45 minutes from Santiago, where in two years there will be world class health care available at HOMS-the Metropolitan Hospital of Santiago. There is also more than adequate educational facilities, and commuting is a way of life to you in the States so a 45 minute drive is nothing extraordinary--It gets the juices flowing... There is also an International Airport connected to the rest of the world-NYC, Miami, etc... I am sorry, I do not like Santo Domingo. It is huge (close to 3,000,000), dirty, and very chaotic. It IS the center of the Dominican universe, but I cannot imagine raising children there, although lots of nice people do it every day. It is also very expensive (I would guess at least RD$50,000 for a family of four:: Say $3,500 a month?) And I could be way, way off, if your child's special needs are really very special. On the other hand, it could be done for a good deal less in the smaller cities, with no decrease in the care provided..
There are local groups for Down's, Hemophilia, and other children's special problems. They are a wonderful, tight knit group of ladies that are ferociously guarding their children's health and needs.
2) Housing. Much less expensive in the North, around Santiago. US$500 can get a reasonable 3 BR, 1 1/2 bath, 2 car garage in a nice area, not far from anything...I am presuming that you will be moving all your "stuff" with you as well as your cars-Now that will be an experience, but it is doable if you have patience....
3) Living. there is plenty to get into here: Intense social life, business, NGOs, all sorts of stuff. You have time to plan...
Since this is, indeed, a major decision on your part, I am sure everyone here will counsel prudence and patience as well as a visit to prospective sites.
Feel free to email me with more questions.
A cordial welcome from the HB