Re: Painting over calcimine
No-one can really answer your question, "will it peel?"
The best step you can take is to use oil-based primer on your work, which will keep water out of the calcimine. That's what tends to cause it to peel. It always remains water-soluble. If you used regular drywall mud to skim coat, that was not as good as using a boding agent and then a lime/gypsum plaster. Still better would be to oil prime before and after the skim coats.
In the future, sc****/wash as much calcimine as you can, then oil prime, then skim coat. You should then be able to prime and paint with anything you like, as any calcimine residue was sealed.
Remove not the ancient landmark, which your fathers have set.