Mom’s best bets are to foreclose from the second position, or let to let the first foreclose and simply bid on the property. This would effectively wipe out any thirds, and in the second position, she would get any “overages” from the sale. Her paying the first to keep it out of foreclosure is a mistake.
From your perspective, if mom can actually pay off the first via a new loan, or at auction, no need to move. She will probably still want a good renter.
But mom really needs to get some professional help to make any of this work, and possible protect herself from what is becomming an abusive son who might see “other” solutions to his problem. There seems to be no limit to the damage family arguments can cause to the family members.