I recently used a latex paint to paint over the wooden kitchen cabinets that had an oil-based enamel paint originally. And latex paint started to peel off when bumped. Can I go over the top of that latex paint layer with an oil-based enamel paint without worrying appealing problems later?
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.
If you have layers A B C D and the layer between C and D is failing... adding a layer E will not help.
Oil isn't the issue. Shiny is the issue.
After 2 years, any paint is finished doing whatever it does chemically, and is chemically inert. So it's not a chemical reactivity issue. Nobody cares that the paint had an oil base.
The issue is that the original coat was high-gloss. (it's a popular reason to use oil paints; oil paints are very good at gloss). And by "oil" I mean alkyds actually.
Anytime you paint, you have the right to do surface preparation. If you imbibe, you are after two things: First, to roughen the surface with microscopic "jagged mountains" so the next paint layer can ooze into these jaggies and mold onto them to get physical bonding. Second, to remove contaminants like grease, dirt, calcium, silicones, etc.
Doing surface prep means the next coat of paint is assured to stick well. You don't have to do it, but if you don't, well... you've met the downside.
I mean you can get lucky; "flat" (as in flat paint) surfaces have some roughness which might suffice, and they might not be contaminated. You alone know the value of your time, so roll the dice. Or not.
Penance for bad prep is hard work
Of course your next question is "What's the best can of product to use for an E-layer to magically fix this?" There is none. The only option for a failing "D" layer because of failure to prep the "C" layer is manual removal of the "D" layer, then proper prep of the C-layer. Sorry.
Fortunately, new latex paint is so soft that my favorite stripper is actually water. Especially over a reluctant oil base. Keep it wet for 5-10 minutes and it comes right off when you go at it with the kind of brush you use to clean the tub. If you need to get into some modest paint strippers to soften it, you can try isopropyl or other bathroom-type alcohols. I wouldn't use anything strong enough to attack the underlying oil paint since there's no need for that.
The other thing about paint strippers is they're not the substance E you're looking for. They're just the first step in an absolutely huge amount of work, and if you are looking for a solution in a can, let's just say you are not prepared for how much work that will be. :) Strippers only soften the paint, you still have to manually remove it, while working in dishwashing gloves and eye protection, then fastidiously wash and neutralize the area to entirely remove all the stripper chemical (or it WILL contaminate the next layer), then if you mottled the surface, you have to prime to level the surface.
Then, when you've got it all off, you try again, this time, with proper surface prep.
And you learn the lesson and don't make that mistake again!
Overlaying different types of paint
To answer your stated question, there are several things not to do. First, don't put oil paint over latex paint, unless the latex paint is very old, it passes a full-on adhesion test, and you do fastidious prep.
Don't overlay paint that is still curing (chemically active). Oil (alkyd) and latex paints take 6 months to 2 years to finish curing. If in doubt, do a compatibility test.