In return, the lender would receive monthly cash flow and a share of the profits upon sale.

It has been 100% occupied and currently returns a positive cash flow of $1,000.

The MIL has owned the property for 4 years and there is no mortgage (purchased in cash by her grandson; I raise this to you in case there are capital gains implications for MIL and DIL when the latter sells). 

I currently have around 200k in cash that is yielding 5 percent in my brokerage account.

I cannot wrap my head around the cash out refinance portion of this situation despite my tireless efforts.

And is it better to be cash flow positive vs have more cash in hands ? 

But, many times the children do not want their parents' name dragged through the mud of foreclosure lawsuits or foreclosure notices, and are also fearful that it might affect their inheritance in any other assets, such as cash or other real estate. 

Cash out 3.

I effectively got it for free and was able to make some renovations as well, now this property cash flows and has great tenants.

I am in this boat as things stand and have a very long outlook on the property that is not cash-flowing.