Is it fair to keep a portion of the prorated rent for the extra paperwork I'm doing? 

In many instances a large portion of the rent is almost guaranteed to hit your pocket each month - again, this may not cover the full amount but they are consistent payments coming in (paid by the government).

Sale the house, use a large portion of the money down along with borrowed money to invest in multi-family apartments?

If the PM has vetted the tenant correctly, they shouldnt have payment issues, especially if a portion is from housing subsidies. 

Also, the existing loan is already seasoned, and a good portion of the interest has been paid. 

So dad gifts a portion of a down payment "many years ago" and doesn't contribute to a single mortgage payment, and now the siblings want 1/3 each? 

Feel free to reach out and I would be happy to help with any portion of the process and I work with all of these lenders on a consistent basis. 

They need an extra $56k to to cover a portion of purchase price and closing costs, monthly holding costs, and the first payment to the contractors(required by first lien lender).

Let's say that you use a portion of your $36k Roth as a down payment on a rental property purchase.

If there is a trust in place, you could look at changing the beneficiary and portions there of.