The Stiff-Leg Deadlift is the exercise is used for strengthening the buttocks and the lateral lunge is an exercise used to increases the range of motion
Three simple hip buttock pain relief exercises can do at home. The wall squat, the bridge and the bird dog exercises are them. I all of them repeated five times daily, you get a tremendous relief from this pain.
You should always check with your doctor before starting any course of excercise. That said, you may find this excercise helpful: Lie on your stomach with your arms over your head, and gently raise each leg in turn.