I replaced most of the walls and surfaces in my bathroom, except
for the ceiling and one or two other small places.

Along with the new drywall I installed, I primed the ceiling etc.
with latex primer. Unfortunately, those places had oil-based
paint underneath it.

I know now that I should have roughed up the surface of the
oil-based paint before I put the primer down. Long story short,
when I applied the final coat of latex paint over the primer, the
primer softened and the whole shebang started peeling away,
leaving me with my original pink, shiny, oil-based paint surface.

So, it looks like I have to take what's left of the latex primer
down and start again on those areas. I want to make sure to do it
right this time.

My question is: what is right? Will simply sanding the surface of
the oil-based paint be sufficient to get the latex primer to
cling to it? Anything else I can do to help guarantee success?

Thanks