“My current tenant gave me 30 days notice that they were vacating the property. I found another tenant and told her she was approved to move in. The current tenant came back and said she does not want to leave now. Can I force her to leave based on her 30 day notice? Does the new tenant have any legal recourse?”
The details of landlord-tenant law vary considerably from state to state. However, if you have a written notice from your current tenant, you can probably insist that she abide by it.
The new tenant may have recourse, if she changed her position based on your promise of a place to live on a certain date. For example, if she gave notice at her current place–and therefore has no place else to live–she may incur hotel costs and storage if the apartment is not ready on time. To the extent that it is your fault, you might be liable for those costs.