Prior to closing the house appraised for $470,000 through a third-party which the bank is now using as their valuation on their website.

It is why assessors and appraisers and banks are always checking "arms length transaction". 

Afterward it appraised at $76,000What was the outcome?

Fortunately, there is a way to figure out what the approximate true value of the property is without hiring an appraiser.

The original goal was to rehab, appraise, and replace the private lender with a conventional loan.If I were to sell, I could initially offer 100% O.F. for about 6 months, then I would need to get enough cash (call that amount 150K) out to pay back my private lender. 

In fact generally an appraiser will have no idea of the difference as there really isn't one.Financing as well will treat your home no different then a stick build, generally there is no variation available between stick & modular appraisals, financing, or real estate agents forms and processes.This is assuming that what you are looking at is a modular and not a mobile or manufactured home.Some of the early modular's had poor designs and looked like a mobile home down to the paneling in the walls.

@Richard Speckman I'm in the process of refinancing my house with a finished ADU and I'm concerned about the appraisal.

You get the credit, Fannie Mae allow full appraisal of the system and the loan is NOT attached to your mortgage or home by lien - there is a UCC1 filed on the equipment only.Leases/PPAs (Power Purchase Agreements) allow the solar company to claim the tax credit.

Hello BP folks,I have an interesting situation for one of my rental property which I purchased in Feb 2016 for $109K.The property has now appraised for $130K and I expect it to appraise at the same rate.

If closing for the cash-out refi is completed at 6 months or greater than the date you purchased the property, it would be eligible for value to be determined with a new appraisal, which of course is beneficial if you have done any work to it to improve the value.