If its rejected, its terminated and the landlord can demand possession.

if you have filed a unlawful detainer I assume you don't have possession of the property.  

I don't want the possession of a credit card to be a filter in my tenant screening.  

Since the property is vacant and the judge awards me a judgement to take possession am I able to start the rehab process?

You can attempt to use these positions to negotiate with the lender to pay the lien off and take possession.

If both parties agree (in writing) to terminate the existing lease then the vacating tenant would be responsible to pay rent up to the day prior to a new tenant taking possession and beginning a new lease.

That works out such that each investor's math would be the following:($140k) capital buy-in for partnership and possession of the property+$95k cash-out from refinance within 3-6 months Leaves ($45k) invested capital in the home, with initial equity at appraised value being aprox $65k.The current tenant is the other partners mother + boyfriend.

Get possession as quickly as possible, clean up the apartment, raise the rent to market, and try to fill with a better qualified tenant -- who is on a month to month rental agreement.  

Contractors that have more time on their hands than work to fill that time - and also possess the necessary skills are eager to do the work at more reasonable pricing. 

I’m no 1031 expert but if you closed last week and have the 80k in your possession then you missed your chance to do a 1031.