Will the courts allow me to move for a new job, if I have sole legal and physical custody of our children?

Question Details: My ex has supervised custody because of drug transactions with the kids present, plus verbal abuse and threats. I was awarded sole custody with supervised visitation that he rarely shows up for even if it is only 2x a month for an hour. I have 3 kids whom I was a stay at home mother to before my ex cheated and soon after quit his job. He made $125,000 a year but stayed at home for a year so when the child support was determined he wouldn't have his past earnings factor in. I get $125 a week for the kids. I work 3 jobs now and still we struggle but I was offered a great job out of state.

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