There are lots of "cans of worms" to open. If it were me, I would look first at saddle: is it level, nose up, or nose down, is it curved or flat? Certain saddles and positions fight pelvis rotation, and make it feel unnatural. What works for me is a curved saddle, set up level (I use Romin's), but everyone is different. Rotating is something you have to practice, but it makes a world of difference in reach and comfort on long rides.

I am a fan of core strength, but it is something, IMO, that helps maintain good position, but not create good position. But I would default to folks with more expertise than me.