Sure, the twigs can go in the regular compost, but woody material just takes a while to break down, wherever it is -- I've found bits of branches in compost that's been sitting quietly for, oh, a couple of years. If you put them at the bottom of a compost pile, they let some air get in to the underside, which helps in composting.

After a little more poking, it looks like I'm wrong about pine needles, too. The problem seems to be not the acidity, but the turpenes in the needles, which should be gone once they're dry (ie once they no longer smell like pine). There's some info on mulching / composting with pine needles here:
Pine needle mulch?

Good luck!