Painting - Kitchen Cabinets

I am currently in the process of prepping my 1940's kitchen cabinets to re-paint (i can't afford new one's), I have found that the previous owner of our house painted latex over oil...shame shame. The latex on the outside of the cabinets is coming off easily with a razor blade in literal "sheets". However, the inside of the cabinets the paint is not coming off as easily. I took a palm sander to the inside of the door & the paint is "balling" up. I'm not real sure if the inside is latex, and or why the paint is acting this way. I am not stripping off the original oil paint, just going to sand, and put on a good primer to re-paint. I want to do this right the first time. I'm tired of all the kitchen items being in my living room, and don't want to have to do this again next year, cause I didn't do it right the first time. (FYI I did totally strip one door face down, to see what the original cabinets looked like without paint, they are good solid cabinets, just not pretty to stain & poly). Any suggestions would be welcomed. Thanks for your thoughts.

Sounds like you are going about it the right way. If you can't get the insides looking great remember they are shut most of the time. When you get them cleaned up use a oil primer [like kilz] then you can finish with latex or oil. Sherwin Williams has a waterborne product called pro classic, it has the advantages of both latex and oil. It dries as hard as oilbase but doesn't yellow or have the strong odor oil has. I assume some of the other paint manufactures have similiar products.