It is somewhat complex to try to explain on a forum, but at a high level, you (aka GP) and your family member (aka LP) would agree on how much the 2 of you would put in for the amount of equity needed (usually expressed as a %).

It's hard to say offer amount without knowing the rehab part since that could blow this out the water.  

BECAUSE if she quit she wouldnt get unemployment on top of the absurd amount of benefits she was getting . ( the amount she gets is between $50k and $70K based on what she showed a coworker) . 

Proportional leverage (like 27% LTV) isn’t specifically required, but if you don’t reinvest the full amount or fail to replace debt, the difference will be taxed as boot.

Self-managing your vacation rentals requires a significant amount of time and effort.

A net listing is a type of real estate listing agreement where the seller specifies a minimum price they would like to receive from the sale, and any amount over that price is considered the real estate agent's commission. 

The fourth loan offer ask to deposit the whole loan amount into a CD.

And as you say it's an UNKNOWN amount, because it's a %. 

You have a 200k equity buffer, so you should be able to get closer to 130k from a LTV perspective - but will your rent amount cover that new loan?

Or should I wait it out a couple of years until I have a larger amount saved up.