Eigenvector wrote:
When installing new window trim for the window sill (that is trimming the
INSIDE) is it normal to apply caulking to seal the gap between the window
frame and the trim?

Will caulking stick to wood with a polyeurothane finish?

Sounds to me like a poor window/trim installation. The trim should fit
tight to to the window frame and there should be no gap. In any event,
caulking sticks just fine to polyurethanes, so if you have a
unintended gap, some colored PolySeamseal will cover iy nicely. HTH

Joe