Hard money = typically make payments during loan period, may be interest only or interest & principal.Private money = can get balloon loan with total loan plus all interest due at end of loan term (which you obviously pay back sooner b/c you sold your property).

If we purchase their home for $40k, they can use that money as a down payment on a new home somewhere that wasn't devastated by the storms. 

There was no accident or are you thinking insure payment/performance?

I ask because a 30 year mortgage payment (P&I only) for that property would be $2,192 with a 3% interest rate.

If the house is not habitable (regardless of the cause), then my understanding is that the tenants do not pay rent during the time the house is not habitable.Hopefully your insurance has a Business Interruption or Rental Interruption clause that you can invoke so that the insurance company essentially pays your rent during the vacancy period.Once the house is habitable, tenants should continue their rent payments.

Please immediately place a stop payment on it and re-issue another one. 

I am interested in a four-plex and using the refi to fund the down payment on one would be a no brainer.

Have them pay you rent until you execute the option, and you pay the same thing to them as your option payments...and yes, make both payments, and keep records.  

If they do not make necessary repairs, make the repairs yourself and deduct from rent payment. 

In that situation, you will have to weigh out the benefits of having that cash available to you versus changing the terms ( potentially higher rates/higher payments ) on one or all of those properties.