smokes, did you have the remainder of the vehicle crushed and sold for scrap? This sounds like a real headache.
I remember that we had to change our drivers licenses within 14 days of moving to CA, or some such nutty amount of time. We had valid MA licenses that had been recently renewed, if I remember correctly. Their website is not clear about any deadlines for changing licenses or car registrations for new residents. It just says you have to do it, but not by when.
We got new licenses (had to take a written test) and had to re-register our cars. The DMV is pretty screwed up. I once renewed my drivers license on line and they ate my money and didn't cough up the new license. I had to prove that I'd paid on a credit card before they'd research their own cockup. That took several hours and I got a newer, even uglier photo to boot. Thanks, DMV.
That place has a culture of incompetent bureaucracy that you can't beat with a stick. I am simultaneously shocked and then again not surprised that they arrested your mother over the "registration non-compliance." That's clearly an abuse of police authority. Christ on a crutch. They could have been out preventing theft and violent crime, but instead, choose to go harass private citizens. That sounds like a nice case for a contingency fee law firm.