Paint after latex over oil base was done?

In this case you probably would have to sand down thoroughly. Latex over oil though is possible but not the other way around

The paint is obviously very poorly adhered to the paint underneath. To best extent possible, you have to remove the paint that is peeling. Any further coats of paint would only be adhered as well as the failing paint underneath.Often scraping the paint will finish breaking the bond. Rather than using a pull scrapper, try bearing down on the surface with a sharp putty knife. Do not push the blade, but rather hold it at an angle to the surface and pull it along the surface. Often this pressure will pop the failing paint.

You might also try "shocking" the paint with a heat gun. The idea is to rapidly heat the failing coat of paint so that it expands and breaks its bond to the paint underneath. You do not want to heat the paint to the point that all the paint starts to lift from the wood!

Chemical strippers would create a real mess. I would sooner re-trim my house than go through that mess!

After you get the failed paint off, start over with a complete prime job with either an oil or acrylic primer. Oil primer can be top coated with either oil or acrylic paint. This old contractor still has a bias toward oil paints on fine woodwork.