I'm surprised that knots are coming through
polyurethane, but if they are there's not a lot
you can do. Bin and Kilz are both pretty good
for stains. They work because the top coat
doesn't redissolve them, so the stain is stopped
at the level of the sealer. But knotholes will
usually come through eventually if the wood
is reasonably fresh. The only good solution is
clear wood. Knotty pine is for "country look"
"It is pine and therefore lots of knots."
Unless knots were intended for "atmosphere"
it's just a case of someone cutting corners.
Decent trim should be at least clear pine. Poplar
is better. Knots don't belong in painted wood in
the first place. And these days poplar is actually
competitively priced with pine. It's usually cheaper
than clear pine, it's less "dentable", and it takes
paint better. The grain is very fine so there's no
problem with grain lines showing through the paint,
as often happens with pine.
If it were me I'd remove the trim and use poplar.
If you keep the trim there's another issue:
Polyurethane is basically a sheet of plastic. If you
paint Bin and then latex paint it won't bond well.
It may peel. It will probably scrape off easily. It
may also shrink away, leaving splits where the poly
(Ever notice how poly over old poly peels like a
sunburn? The may be both poly, but the old layer
is cured to a sheet of plastic, so the new layer
doesn't properly bond.)
Whenever I need to paint or poly over cured poly
I first wipe it with sanding liquid. I mean the fumey
stuff, not newer versions. The sanding liquid softens
the surface, making it as though you're painting over
fresh poly, so that a new layer can bond to it. (It's
ssomething like dilute stripper.) I would then prime it
with something oil-base -- Kilz would be OK. Oil base
underbody would be much better. (Benj. Moore makes
one.) After that you'll have a surface that acrylic paint
can stick to.
Bin is pretty good for spot priming but it is a sealer.
It's not designed as an underbody or primer for large