Unless your daughter had a written lease that addressed this issue, this is a difficult issue to address. Your daughter could sue in small claims court to recover, but it may not be worth her while and she may not win.
If rent pay day is the first of the month, and the landlord gave notice (which needed to be written) on June 2, then you do not have to leave until the last day in July. It is 30 days from the next rent due day, and the next one is July 1. This is per the Arizona Residential Landlord-Tenant Act, which the landlady must abide by whether she likes it or not. There are also procedures for protecting your security deposit in the Az L-T Act.
If your daughter paid rent on the 1st, the notice to vacate on the 2nd extends the lease through the following month. The landlord cannot change locks on the 15th or apply rent against cleaning fees if this was not part of the lease.
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