Is it illegal for a person to have two apartment leases signed at the same time?

A person can have as many leases signed as the person can find landlords with whom to sign the leases. That is, it would not be unlawful that a person is the tenant for two places at the same time. Your friend should keep in mind that if she is the tenant of both places, that she is liable for whatever she agreed on each of those agreements.

As long as there's compliance with the leases, there's nothing illegal about it. It sounds like the landlord allowed substitution of the mom as the actual occupant, and since landlords often do restrict subletting and want to know who's actually residing in the places, as long as they know and have agreed, then there should be no problem. The landlord consents to changes in occupants should be writing in the form of an amendment to the lease or at least some sort of acknowledgment to protect against later claims. Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.