I worked for the IHS for nine years in New Mexico and Arizona.
I enjoyed the work,was able to train in the area I desired and gained experience in ways I would have been unlikely to do in other setting. I grew to love the area,landscape and culture.
That being said there are things you will need to realize aout this very different work setting. First, you are in someone else's culture and you must respect that and adapt to the way things are done there. Many of the areas are very remote and you will be a long way from amenities. The housing available at some locations is limited and may not be up to the standards you are used to or if near the edge of reservations you may need to commute 30-50 miles to work if you live off the reservation. Unless your spouse is also in healthcare there is unlikely to be local employment for them.
As for your children, it is a mixed bag: academics-wise the schools
tended to be somewhat behind the average grade level in teaching. Many people opted to send their kids to local church run private schools. It is however a great value for children to learn about living in a different culture. My son was cared for by a local woman while I worked and was just "thrown in" with the rest of her kids so was able to experience much of everyday life there. Even what seems very negative - the fact that he was the only "Anglo" child in his grade and did end up on the receiving end of quite a bit of racism and poor treatment from some kids - did in the long run prove to be invaluable, as it taught him a perspective that he would never have had elsewhere and helped him to grow up with an awareness of how hurtful such behavior is.
Although it seems I have written much negative, I would go back in a minute. I left only because of a desire to travel and do take jobs back out on the res when I can to reconnect with everyone.