Can I paint over latex with oil-based enamel to repair a peeling situation?
Painting over paint is never a good idea especially on something like kitchen cabinets that will experience a lot of wear and tear. If you're looking for long term results, strip off the layers of paint with a good paint remover and repaint with a quality wood paint. 

There are many paint removers on the market that are very easy to use and you can complete a project fairly quick. One that I have used often and can be used safely indoors is Citristrip. Brush it on, wait 20 minutes and wipe it off.