Painting Over Old Plaster and Drywall?

I have a 1950s plaster/lathe home where the bathroom was done quickly-not necesarily correctly, and now I the new owner; am re-doing it with twice the effort. First-they painted latex over oil; so I am stripping all the paint off the plaster as it was cracked and bubbled. But where they replaced the bathroom fixtures, instead of dealing with the plaster and having the plaster repaired-they cut it flush and butted drywall up against it.

So-there are many walls where I have plaster for the first three feet that must be stripped; then I have drywall that is not peeling or bubbling and does not need to be stripped-and actually would do more harm than good to attempt to strip the latex paint off as the drywall would peel and rip if I tried to remove the paint.Question is, if I plan to prep the old paster with oil based Kilz prior to painting, will the oil based Kilz cover and seal the old latex paint that is on the drywall effectively? Or will I be dealing with bubbling and peeling from the oil based primer over latex in a few years? I know I can paint the final color-latex coats of paint over the oil-based Kilz after it is properly primed and cured on the plaster-but what about putting the Kilz over the existing latex on the drywall? Thanks!

By Sonja R