I'm sorry to hear about your son's difficulties. Unfortunately, transferring his probation won't be an easy process. There are a couple of things to consider:
First of all, if either of his convictions was for a felony, any probation transfer would have to be approved through the Interstate Compact, which controls transfers between states. The transfer process can take six months of more, and California and Kentucky would both have to agree.
Second, the requirements for domestic violence probation, set forth in California Penal Code §1203.097, are very specific. It included the the requirements for the counseling program, which must be approved by the probation department and is required to make monthly payments to the court.
Your son might want to return to court and request a "terminal sentence," or fixed jail term, instead of probation. That way, when he is released, he wouldn't have to worry about probation or the domestic violence program.
It sounds like he didn't have the money to hire his own attorney, so he was probably represented by the Public Defender. The PD would rather talk to him BEFORE he gets in trouble for a probation violation, instead of trying to help him AFTER he is arrested for failing to complete the class. He should go to the Public Defender's office immediately and ask if they can help him find a solution.