If paper is sound and holding tight,proper skim coat is best use of time and labor. It really sucks that you must approve anything they do and how it's done. Paint they apply over their skim coat might effect adhesion of new skim coat so you would be better off if they left it alone.

It Has been skim coated and painted. But something else must be done to improve the look of the walls. Are you saying that another skim coat may not stick to the paint?

That is exactly what i am saying. Depend's on type mud and paint. Are you planning to tackle this yourself or geather information for the professional you hire?

Planning to tackle it ourselves.

They used drywall mud and the paint they used was Sherwin Williams super paint.

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If they are not doing the walls right, are you sure that important stuff, like wiring, and plumbing, and structure, and roof, etc, are being done right. Its all something you need to look into. It may turn out to be a money pit for you, or a really bad renovation, that you really do not want to deal with.

Good point cat. Most unusual arangement. I'm accustom to sellers giving buyers a repair allowance at closing or working off buyers scope of work if doing repair between signing contract and closing.

Yes, that would be preferable to me too. The skim coat is usually done by a professional, and should have been done right. This sounds like a diy gone bad, so it makes me suspect more important things, like electrical, and plumbing and roofing, etc..

What kind of paint can't you skim coat over? I would think that if you sand any wall that is painted, you could then skim coat over it, assuming the paint is adhering to the wall.

The house was Donated to the historical society who did repairs before selling. We did do inspections and electrical and plumbing look good. We thought the historical society would know what they were doing.

"We thought the historical society would know what they were doing."

They know what they are doing,so does anyone that has bought or sold a piece of real estate. They are "putting the screws to you". The evidence point's to you being the one who doesn't know what they are doing. If you don't have a realtor repersenting you in this deal,I reccomend you stop worrying about wallpaper and get one right away.