Child request to change residences

My step-sons are 10 and 8 and have repeatedly told us they don’t want to return to their mother’s house from their visitation with us in New England. She is unstable at best. She is going through her third divorce, at age 32, and has moved the children to their fourth home in as many months. She admittedly uses the child support money to fund her own desires and often relies on others to support the children. Her estranged husband feeds them several nights a week as per the children, she doesn’t have the money to buy food. Her parents also support them with clothes and other items the child support is supposed to fund but because of her abuse of the money, doesn’t. My point with the explanation is that the children are fed up with her and on Wednesday tried talking to her about moving to New England with their father and I. She dismissed their feelings and told them under no uncertain circumstance will she allow that to happen and punished them by continuing to yell and sending them to their room. I’m not saying she is abusive or neglectful as it appears by one way or another the children have the material things they need, so a GAL doesn’t seem to be the appropriate solution, although we are looking into it. My question to you is how do we go about getting the children up to New England with their father and I, to a stable house-hold, permanently?

File a motion to modify custody based on her inability and lack of desire to care for the children…