I am a residential designer based in North Carolina, looking into either pre-fab or shipping container homes to rebuild/replace homes in PR.

When you have an appraisal the appraiser looks at what tr would cost to rebuild.  

You must ask for a rebuild letter for the city/ county .

So does rebuilding a 4-barrel carburetor.Once you get into rebuilding that carb, you'll find that there are a hundred little pieces and parts that you need to keep very good track of, or you'll end up with a pile of junk and a car that won't run.Selling real estate is the same way. 

Buyer paid 95k and now gutted everything and tore off the back and is rebuilding., wheras this house was totally livable.

Just let it go rebuild your credit and buy something else.  

There are places where the price of SFR are so low, that vacant lot would not make much sense since any attempt rebuild would be too expensive.

Would it be more profitable to just doze it and rebuild?

First, the father wants to move a small 8x6 shed that is in the "middle" of a rebuild onto the property. though my lot is only .31acres, i do have enough room for it next to my current shed, or even in their separate driveway, does this sound like the beginning of a horror story ?

What will it cost to tear down, What will it cost to rebuild the house, What can you sell it for afterwards.