All of that peeling paint has to come off if you want a new coat to stick. Practically speaking, I'd explore buying new doors rather than trying to strip that much paint. It's just a horrible amount of work. The only time it's worth doing is if there is some historical significance to the doors, like they are the original quarter sawn oak or birds eye maple that some previous owner stupidly covered over with paint. The other issue is that the doors are the most expensive part of cabinetry, and if you're ponying up money to replace those, then for just a bit more money, you can probably replace all of the cabinets. It's the want of that single nail that defeats the whole king's army you know...

Take one door off and try the shorter method and see if you can live with it, that will be the best way to decide. Then go to Plan B of live_wire_oak .

If you decide to give one door a try you might want to try the new Benjamin Moore Paint called Advance. I learned about it on a blog where a woman was using it to paint furniture even though it was manufactured for cabinets. It lays smooth with no brush strokes. I've just bought a quart to try on some furniture I want to paint. It's not cheap, but for me if it makes my work time less and looks great, the cost is worth it. Good luck.

I wanted to add, it's a water based paint and very low VOC's.

Tinan unfortunately this is what happens when someone does a quick slap of paint and skips over the prep work, or uses an incompatible paint. Do you have a heat gun? I've scraped off many a coat of paint from furniture, trim, doors etc with mine and it's not really hard work, just a heat gun and a paint scraper, and then a quick sand and prime/repaint. You could always just give it a really good sand to cut back into the bad paint layer, but I find stripping off the paint with a heat gun is just easier and tends to give a smoother finish.

Oh dear I was afraid that would be the answer. The cabinets are the original horrible MDF from 1980. I would love to replace them but we need to get another couple of years out of them - not in the budget to replace them yet. We just had to put in a new furnace, that was a higher priority!

Yes the PO slapped white paint - probably a cheap grade - on to dress it up when they were selling.

So my plan was to make them look decent for another 2-3 years and then we will replace all the cabinets and the old tile countertops too.

I don't have a heat gun, and I'm concerned that that would cause fumes? I wonder if the paint underneath is oil based and that's why the top layer is peeling. I'm very sensitive to fumes etc.

Well what's the worst that can happen - it starts to peel again. Maybe if I sand it with rough and then fine grit and try the Advance paint it might stick for a while!

There is a slight bit of fumes when you use a heat gun but it's nothing like the fumes from painting so I just wear a mask and I don't notice it. But if you just want to clean them up for a year or two then yes, just sand them with a coarse grit to cut the paint back and clean them up, and then with a finer grit, and then use a good quality primer. Even if it was oil based, it just needed proper prep before they painted it and the paint would have adhered properly but it could have just been dirty or too glossy when they painted over it too.

If that's MDF, then you don't want to invest a lot of time or money on stripping - and I'm not sure you can use a heat gun on MDF. I would sand and then apply a good sealing primer - maybe something like Zinsser Bulls Eye 123. For the topcoat, you might consider Cabinet Coat. I use it on my trim and cabinets.

I would just sand very well and sand lightly between coats. I think Graywing's suggestion of a top coat is a good one.