You should have primed the trim with an oil base primer. This would have prevented all of your problems. Basically you did 2 of the 3 preparation techniques needed; (1) clean, (2) sand and then (3) prime.
I never trust any paint to be self priming over varnish, old or not. Always use an oil base primer first.
Try doing all of the prep needed, including priming, then apply your water based paint. See how this work out.