Why is the primer peeling off like plastic, and what can I do to fix it

It sounds like the dampness is still a problem in that particular area because it is a corner adjoining the external wall and the store area. Is this part of the house in shadow for a lot of the day?

1. Check the external ground area surrounding the outside store. If the ground is clay or compacted it might not be helping in that it is storing water. Perhaps better drainage there.

2. Some form of heating in the store area to keep it at a similar temperature to the kitchen e.g. condensation happens in that part of the kitchen because of the cold store area on the other side of that particular wall.

3. Perhaps a better seal on the door and windows in the store to keep it warmer in general.

4. Put a faux wall in the back of the store to buffer the cold air away from the wall that is adjoining the kitchen.

5. A robust kitchen extractor to remove as much steam as possible from cooking.

Definitely read up on the EPA 'renovation repair and painting' rule.

Option #3, the 1/4" drywall, is likely to produce the best and cleanest results, at the cost of loss of room space and alteration in the look of all your trim. You'll have to extend all outlets also. Of course that sounds suspiciously like what happened last time. Eventually your room will be solid wall covering with no center.

Option #4 sounds attractive if that texture on the wallpaper will really hold the joint compound. I'd run a test with and without the primer/sealer. Remember worst case here it cracks later and you redo it all with #3.