Victoria, you'll find all the information that you need in the archives if you search.
Regarding residency and being able to work, I would suggest that you think of visiting a good attorney when you are here to discuss the process of residency. A good attorney can make the process easy. It is not hard, it just takes a little time and is much easier if an attorney leads you by the hand and clears the way for you. I cannot imagine sitting and waiting in the long lines at the various departments sometimes for days, with four small children. Of course you can try doing this yourself as well. The information is in the archives.
I suggest also that you consider visiting some of the regulars on the board when you are here, to hear first hand experiences of living here. Most of the regulars will respond to an invitation for coffee or a Presidente and a short meeting. In addition to doing your research, this will give you good insight.
In short, medical and dental care is available and quite excellent if you go to the right places. Good schools are available and expensive in DR terms.
Regarding your husband's work, I quite frankly do not see this as a viable way of making a living in the DR, or even just keeping some money flowing in. I don't see sufficient numbers in the Canadian/American expat population to make this viable and I can not imagine the larger german population making use of counselling services. Folks here are generally happy to be what they are and are somehow self-reliant. Nevertheless a friend of mine would have used this service a while ago to assist his Dominican wife who had problems. I cannot comment on availability of teaching positions at a University but I do know that you need to be fluent in Spanish to consider this. Workshops for businesses also require fluency. I also don't see this as a viable income generator.
Having said all this, stranger things have happened in the DR and who knows, you may beat all the odds. It is a good thing that you come here for three months. In your position, it would be good to stretch this period before making commitments. Do your research beforehand, talk to a lot of people and go to a lot of places when you are here.