Another good glute/hip exercise I forgot to mention is bridge. Make sure to keep your pelvis level. For an advance move, try lifting one leg at a time, but only if you can continue to keep your pelvis level.
I'll have to try side plank with a leg lift. In yoga, I avoid side plank since it hurts my hand and wrist way too much. I could try modifying it by doing it on my elbow (which is not how you'll see most yogis doing it in class). Is that what the OP meant by "half side plank?"
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher