Sounds like the original vinyl paint was put on to bare plaster without a priming coat. Some of the paint has stuck to the plaster and some has just formed a paint film hardly attached at all - it is best to slap on a coat of thinned paint that can soak into the plaster, you get better adhesion when the top coat is applied.
From what you say I suspect you will have hard edges between the existing paint and the bare plaster - even if you were able to paint over the whole there would be raised edges where the old paint lies under the new.
Get the wall smooth before attempting to put a finish on it. Prime. Paint.
Richard Buxton, September 2008