I would like to put a loan on the property to pull out as much of my cash as possible to use for other property investments. 

Sounds extremely suspicious to put it very nicely. 

Vesta can then pursue the lien and the fees or it will eventually put it up to the Sheriff to auction.  

Don't get into the whole story when you call these places just tell them you're a new homeowner, the last owner didn't keep good records and you're putting together a binder of service records for the home so you can get ahead on maintenance.

Unfortunately she just hasn’t quite reached the 2 year minimum yet so we’re just trying to figure out if she qualifies for a partial exclusion (doesn’t sound like it), or maybe an exception due to one of the circumstances outlined in Publication 523, or she may just need to wait until after October to sell (1031 isn’t an option as it has never been an investment property, installment sale or putting it in a charitable trust would not work either  as she needs the funds immediately for the next purchase). 

I am looking at purchasing a modular home, but has two repairs that it needs first has some soft spots in the floor would it be easier to put new flooring on top or just cut out the soft spots and replace them?

This put is substantially behind on bills and our mortgage.

A cash out refinance to buy more property would put a substantial dent in cash flow with current interest rates.

For example, could you scale and have the security of modest cashflow (somewhere between 2-5% after all expenses, including CapEX are accounted for), if you put 30% down? 

My fear is that acquiring a of couple properties with a mortgage and then BRRRR later will likely put us in a position where we won't have as much cash left for an "all-cash" purchase and then BRRRR.A few other points for context:1.