The checking account that your SS checks goes into, make sure it's only SS checks that goes into them, else they garnish everything. They can't, or not supposed to, garnish proceeds if it's from SS checks.
However, there's been an investigation in my area about collection agencies and law firms playing dumb seizing monies from accounts anyway that they clearly shouldn't, and it then takes debtors months to get the money back, and only after debtors get hold of lawyers.
As to the account under your mom's name, and SS#, from what I'm told, it's considered your mom's. She, or you, might play it safe to open one where it's her name only, and you the "power of attorney" only, so you can help with the banking. My wife does banking for her aged mom, and some accounts are joint, while others are done as POA's.

