OP - Focusing in on the oversold flight, it is likely that US DOT rules will be more generous here and will apply to AS as a US carrier. The compensation for involuntary denial of boarding due to an oversale is 400% of the cost of the ticket segment, capped at US$1,350. I don't know what the segments cost, but you can calculate that. Hopefully your travel insurance will cover the lost prepaid hotel.

As to the rest, if you knew that you had been rebooked onto AS, you should have gone to AS first. If you were unsure, at least call ahead to ask.

Yes, AS ought to have asked for volunteers and it ought to have off-loaded passengers in a pre-determined order. I am not certain why that was your family. But, that will not affect your compensation.

I would file a request with AS for the IDB compensation, ask to be advised within 7 business days and, if you have not heard, file a US DOT complaint (easily done on the website) on the 8th day.