My question involves a marriage in the state of: Connecticut
My husband was married and divorced in CT 4 years ago. His alimony is set to expire in a couple of weeks. Soon after his original alimony/CS order was finalized, he was laid off from his job and had trouble finding permanent opportunities. He moved out of CT and went much further south to lessen his cost of living, but obviously decreased his visitation and added high travel costs. He was self employed up until last month so his income fluctuated greatly month to month, making consistent payments difficult, so he has a decent arrearage. We married the same year of his divorce and welcomed a son later that year (unplanned!), which further lessened his ability to pay the full order amount. He requested a modification 3 times with no results, even though the variance in payment was greater than the 15% threshold per CT's modification rules.
His ex-wife has been living with my husband's parents since their first year of divorce (a multi-family property), which has been a rent-free, utility-free situation. Alimony was ordered for her because she lacked an education. She has taken a few courses at her local community college over the course of the last 2 years, and had received grants to do so. She actually received a surplus of grant money when she didn't take a full course load, and used that money to take 4 vacations the summer of 2011, while the kids were with us for the summer. She started working as a cashier at a pharmacy a year ago and doesn't show any signs of growth.
Given her living situation post divorce, and slow educational/work pace, would he have a case to negotiate his alimony arrearage down? He has tax returns for each year to prove his inability to pay the ordered amount. More importantly, will his arrearage affect his chances of going for physical custody of his eldest child? Now that he has a steady income and the alimony portion is expiring, he is able to return to weekly payments, will pay over the CS amount to chip away at the back-alimony and hopes to build a good case for custody by next April when his son turns 12. His son has continued to struggle socially in his current environment and is better understood/handled by his father. I should also mention that his ex-wife is still without a driver's license, a promise that she has broken each year since the divorce. She and the kids rely on family for transportation. It's not a great living situation for them, and as they get older, she seems less equipped to raise them, as she is still very immature and dependent herself. If she's incapable of providing for herself, why should she be able to maintain custody of two kids if the father has the desire and ability to take on physical custody?
I realize this is a two part question. Appreciate any advice on either parts.

