I have tried vinegar in the guest bathroom. It seems to work somewhat. However, it appears that the sticky side of the wall paper (white) remained attached to the wall while the decorative side peels right off.
Should I simply paint over the reaming sticky side with the paint (or possibly with white primer first) OR should I try to remove the white, sticky side of the Wall paper as well AND with what?
Try DIF. You can purchase it at the hardware store. I prefer the bottle of concentrated DIF. Mix it with water and put it in a paint roller pan. Then take a rolling brush and brush it on the wallpaper to saturate it. Let it sit for about 5 minutes (making sure it stays saturated) and then peel it off with a scaper. For difficult wallpaper, they also sell devices that scour the wallpaper with tiny holes. This helps the chemical seep down to the adhesive.