If your mom is moving back in with you, she has to sign the lease, and she will be "jointly & severally liable" for the rent under the law. If you don't pay in full on time, they can go after your mother, too.
A "preference" is only that. She cannot deny renting to you because you are a household of 3 persons instead of 2, unless there is an occupancy permit on the property which limits occupancy to 2 persons. She can turn you down because there's another applicant with better credit rating, landlord & character references, and/or more adequate income. So are there other applicants to rent that property?