Dear Alex
Your first mistake may have been that multiple stainings. Stain contains a binder agent (like glue) that may not have dried properly with this multiple application. You would have had to wait 24 hours or more between stain applications. I use a better stain brand like the Dura Seal stains when I want a really dark color. Their coffee brown is very dark and rich, and one application always does it. You also may not have waited for each coat of poly to dry, and you may not have scuff sanded thoroughly between coats. I never use the Minwax brand, and prefer the Fabulon brand heavy duty poly instead.
The dry times listed on ALL these finishes are WAY too optimistic, and I always let stains dry at least 24 hours, and wipe my hand on them to check for transfer. I also smell the stain, to see if it has lost all solvents. I BRUSH on the first coat over the Dura Seal stain carefully, and let it dry 24-48 hours. The test for finish dryness, is to screen or scuff sand and check your screen for any gummy transfer. Also smell the floor, any solvent smell and wait another day.
I would never recommend a moisture cured poly for residential use. The toxins in that finish are most awful. You are severely poisoning yourself every time you use it. It's for industrial use only. And they will never perfect the satin flatteners in this type of finish. We only use gloss, with MC poly.
The Fabulon Brand has a very reliable satin or semi gloss finish poly that I use all the time, with great results. But I brush the finish on, I never use lamb's wool applicators. No bubbles and a even sheen is my result. And happy and paying customers also.
So my advice for peeling finish, is to have the floor professionally sanded again and start all over with the finishes and methods I suggest. You will get a more consistent result by sanding all the floors in the house, staining all at once and finishing all at once. Store your furniture and bite the bullet, and hire a pro at least for the sanding, but you certainly can do the staining and finishing of the floor yourself.
Oh, and don't expect any oil modified poly to cure until a month has gone by. And, very old finishes are harder due to the fact that they continue to cross link throughout their life, until they finally become brittle and crack. This takes about 40 years, so don't worry about it.
As always your Most humble servant, Joseph, the Wood Floor Doctor.