We fear the tenant will stop paying and never leave. 

If money is an issue, right now leave it as it is, and do it when you make some money from the venture. 

How / why is she leaving the previous place?

Like @Mary Mitchell my vacancy rate in Brooklyn, NYC, is effectively ZERO.I have been owning rentals for 21 years, currently have almost 30 apts with about 70 tenants.I estimate that I probably lost around 5 months of actual rent in all of these years.The vacancy rates are so low, it is SUB-4%.Normally, I will get a 45 day notice from the tenant leaving.

This is very likely a tenant that will leave when presented with having to pay market rents.

I would then be able to do another 70% LTV against the newly renovated $100,000 property ($70,000, pay off the $28,000 first loan leaving me with $42,000).I should be able to rent each for about $1,000/month after renovation.   

You need to leave a reserve knowing that. 

So my cousin was telling he knows someone selling a house for $500.00. The home has fire damage so it has been gutted will need new wiring all throughout. A tree feel on the garage garage is still standing though. As ...

We've butt heads a few times, but I leave them to their job.  

If they leave I would like to charge more so that is why I am asking about your experience and location.