It depends on how much furniture you have to move.

But I wouldn’t move. After the Trustee’s sale, chance are good that you’ll be given an incentive to move. Otherwise, the bank (if nobody buys the house at the trustee’s sale) will have to proceed with an unlawful detainer to evict you.

Can your mom move in with you temporarily while she looks for a new rental? It’s much easier to find a rental if you’re not stressed about a roof over your head.