If I understand what you mean about putting my hands on my hips, then my thumb lies directly over my sacro-iliac joint. It is not you spine, it is where your spine joins your pelvis. Your glut max attaches to the inferior border of the iliac crest and has quite a big attachment.
Sacro-iliac joint problems are generally caused by stretching for an object whilst you are bent over. It goes stiff when you don't move it and doesn't like being slouched. So this fits in with first thing in the morning pain as you are stiff from not moving over night. This is either the same for sitting, or you are not sat with your bum in the back of the seat allowing posterior tilt of the pelvis that put stress on the sacro-iliac joint.