Despite my concerns, I allowed the appraisal to proceed.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

When that portion was complete, I could then receive draw money which allowed me to pay my utilities, taxes, and mortgages.

It ends when they AND their stuff is removed to the level that allows you to begin the re-rental process. 

,Renting your primary home back to yourself isn’t typically allowed by the IRS for tax purposes, even if structured through an LLC.

That will allow you to build the additional legal space further amplifying the value of the proprety (more HELOC money). 

(for instance, this property has a backyard that could become parking; however, there is no way to access it unless the neighbors allowed us to use there driveway to get there).* Are there any other downsides I might not have considered with street-only parking?

Her mother is willing to (co-sign) and has excellent credit and debt to income ratio that will more than allow but I’m not sure the best way to structure this for the house to still be in our name?  

If both the parent and child are married, this allows forgiving up to 4 times the annual gift tax exclusion per year.

The sponsor if they even consider allowing you would be a huge red flag for me knowing if they will accept non accredited investors what other rules are they breaking. 3.