We recently purchased a great 1960's home from the original owner. None of the wood trim/molding has been painted. It all looks as though it has some coating (polyurethane?) that is still slightly shiny.

I have already attempted to paint trim in two bedrooms following the steps listed below. The first room yielded a good-looking finish (likely due to the quality paint), but one that chips and peels down to wood with even the slightest scratch of a fingernail. The second room with primer only responds to light scratching in the same manner. I have stopped all painting/prepping in order to find the best method before I proceed any further. Any specific tips and processes for how to paint this wood trim would be greatly appreciated!

Painting steps I have followed:

1. Clean baseboards and trim with damp sponge

2. Prime one coat with Benjamin Moore "Fresh Start"; dry time approx 10 hours

3. Paint one coat with Benjamin Moore "Advance"; dry time approx 18 hours

4. Paint second coat with Benjamin Moore "Advance"; dry time approx 4 days