And keep in mind that the rate on the 2nd lien will likely be 10-12% so depending on the cash flow it might not actually yield that much cash to you at closingMore importantly, it's just more debt so ultimately it sounds like you need an income-producing event to actually improve your situation and avoid some of the consequences that you mentioned

780 or higher should get you the best rates/terms available, no difference than 820 score.

Are there lenders that will lend on the product at competitive rates that are similar to current 30 yr sfh amortization?

However, for longer-term profitability, flexible loan terms often have a bigger impact, especially with interest rates or repayment structures that align with your goals.

Aside from restrictions, the thing that is surprising me is the low cap rates. 

But you can look up vacancy rates on websites like rentcafe or rentometer.  

We also get to enjoy our place as often as we like (the slightly lower occupancy rate due to our use is also a factor in being cash flow negative) and the negative cash flow is offset easily by the equity we'd gain, even assuming only a 2% appreciation on the cabin. 

I would look for a bunch of Sub To Deals with 2-3% interest rates ...... then rent out for cash flow and huge equity build up when rates are really low (check out amortization schedules and compare 2-3% vs 6-7% with the same balance and length of time - check out the principal portion each month - the lower the rate the higher amount goes to principal PLUS better cash flow).

Not sure, from what you're writing, what the benefit to the borrower was in refinancing, but there had to be something; cash out and lower rate are two that come to mind. 

Although you plan on having your mother live in the home to start you'll want to assess the home using the current rental rates and values in the area.