After my second child I had a lot of burning pain in my hips and back. I went to PT when my old stretching routine didn’t work. They gave me some pilates based core exercise (laying on my back knees up and contract my abs around like a clock stopping at each hour for a count of 10-15 sec) and suggested just walking slowly on the treadmill, for 5 min per side, sideways. It really helped. I have a sway back as well.