Painting over latex and calcimine
Painting over calcimine is a nightmare anyway, and you've got double trouble since someone previously did it the wrong way
Normally, re-coating a calcimine ceiling would be to use a calcimine re-coater (essentially a flat oil-based paint) and make a small offering to the Paint Gods and hope for the best
Short of over-rocking (putting a new sheetrock ceiling right over the existing), your best best is to remove any/all ill adhering coating ("scrape and sand"), and CalcCoat what's left, and hope what's left of any (if any) latex is penetrated enough by the oil CalcCoat to help it stay stuck
If ALL the latex comes off, frankly you're in a much better spot, so go with it...
(It would be a good thing if it's at all possible...so it would be a good goal here)
Even if all the Calcimine comes off, yes (!!!), you should still CalcCoat anyway