Lots of good advice. A competent appraiser should be able to provide you with an appraisal the will estimate the value of the subject, if completed along with an estimate of the cost to cure various projects. Personally, I would recommend filling in the pool are as the cost to complete will not be realized in market value in Michigan. I would also bring in a builder and/or home inspector to completely go thru the existing structure to make sure everything is up to code, all needed inspections have been completed and approved, that all required permits have been obtained, to let you know what they fell needs to be completed, etc.
As others have stated the appraiser’s estimate of value is most generally based on gross selling prices. The seller is going to be responsible things like real estate commissions, owners title policy, transfer stamps, shared closing costs, possibly survey, corrections based on buyer’s home inspection, property tax proration, attorney fees, special assessments, condo fees if it is a site condo, etc. These expenses could add up to 10% or more of the appraised value. To say nothing of the capital gains tax you could be responsible for should you decide to sell the house. The other thing I would be careful of is supplier and/or labor liens. There maybe some outstanding bills from people who may file liens, or even friends who did pro bono work and are now going to file a lien for their services.
If the other sides believes your offer is too low and want you to pay more, you can say ok I will sell my interest to you based on your appraisal. Sounds like they may not be able to do that so that would only improve your bargaining position. Was a lender involved initially, if so what was the original estimate of value based on your plans and specs? That may be the person to discuss a cost to complete value.
There used to be an appraiser who was active on the forum and I believed to be very knowledgeable. He works SE Michigan, but I am not sure if he works in your specific area. His handle on here was Michigan CG.
Chances are good if you honestly explain the situation to any appraiser, many will probably turn down the assignment as they want to avoid possible depositions and court appearances.
Good Luck