Step 2- close and start rehab-- would need to pay holding cost during rehab?

Ignore the $1,250 per month because that's your cost of housing, if you didn't pay that on the home you'd have paid that in rent so that's a non factor. 

A longer timeline will make paying the extra 2% now more attractive.

This would likely take coordination with a tenant at some point - (ie - plenty of notice to them that they must vacate in order for you to sell the property)Since your current home is free and clear -  you could do a cash out refi or take out a new mortgage on the new house to be able to buy your paren't house and pay off the mortgage.  

if he performs a service for you, just pay him for it. 

Our current mortgage terms include a late fee after 5 days, so they’re already paying extra each month and have to split the total monthly payment up between 2-3 payments when they get their pay check.

The guests refused to pay.  

The only way to pay down a loan, is to pay down a loan.

How much do they want you to to pay, to pay off one of the mortgages (or both of their existing mortgages)? 

Risks: rates go down and you have to pay a prepay of 2 or 3 %; you have to sell and pay the prepay; rents decline & you can't make the payment like any other type of loan; cost upfront a little more than conventional; need to find experienced broker licensed in the state where subject property sits; servicers are bulldogs.