The hip clicking can technically be explained by this particular problem. When that muscle gets tight, the tendon is more prone to flicking quickly over one of the bony bits at the front of the pelvis. This frequently causes pain and can cause a sensation of something moving in the front of the hip.

There are other causes of the clicking hip of course.

One is the iliotibial band (ITB) that causes snapping on the outside of the hip. The last is that there is something disrupting the internal mechanics of the hip -- like a piece of bone, cartilage or something else. If the exercise programme does not work, then I would advocate a CT/Wikipedia reference-linkMRI to just clear something like that.

Hope you find some relief from this.

Cheers,
Quickstart