The judge would likely grant 6 months of supervised visits with a psych eval. However, the Judge in family court rules for what is in the best interests of the kids...even if that's not what the parents want. He may find that your ex is too volatile right now for visitation.
As to your move to NH, you will have to ask the Judge's permission for the move. As long as you have a job and place to stay up there, and some sort of support network (such as friends, family, or even just a good job), there should not be a problem.
Legal custody is the right to make major decisions in your kids lives. Can your husband be reasonable about the kids or is he always a crazy person? If he can be reasonable, then you can share legal custody so he has a say about where they go to school, to the doctors, and other big decisions. If he is unwilling to cooperate with you even that far, then it may be for the best that you have sole legal custody for the time being.
It may help you to find an attorney who can at least advise you. There are many options for low-cost or free legal services for people who qualify. Try contacting the Volunteer Lawyer's Project or your county bar association. If you don't quite qualify for free/low-cost services, there is also the possibility to take advantage of MA's new system of Limited Assistance Representation, in which you can hire a lawyer to do just one thing for you. You could pay for a few hours of consultation, or for an attorney to accompany you to just one court session.
Best of luck in this situation. It seems, from what you've said, that this change is for the best for you and the kids.
If I understand you, the father is still with an interest. Having said this, you cannot relocate without his permission or tht of the court.
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