How to fix vinyl silk painted on plaster??

Try peeling off what you can. Very light use of a stream stripper could help in doing this as it will lift the edges of the paint allowing you to further peel areas of paint (be carefully to allow the paint/wall to cool down from the heat of the steam first) . Allow the wall to dry. Then apply a thin layer of good quality internal filler (I recommend Toupret) around the edges of the paint you can't remove and to any areas that have been marked/damaged during removing the paint. Sand smooth and hopefully you will then have a surface ready for painting again DO NOT use PVA. Use a paint suitable for new plaster, it acts as a primer. I usually apply sufficient coats to obliterate the colour of the plaster. Then paint with your chosen emulsion but it's worth diluting the first coat (the recommendations for dilution should be written on the instructions on the back of the tin. Hope this helps

If you can literally peel off the wall then you should peel off the wall! Otherwise if it has adhered I wouldn't panic too much. You are right about a mist coat. Top tip, let coats dry before panicking.

Peel off what you can and coat with a pva and water to give the fresh paint something to grab too Maybe a light sand down over the areas to be painted to open the areas up if over polished plaster before the pva