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" decorating.
"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 shows through. (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 areas.