When you say "can be felt more if I apply pressure to the outside of the joint (somewhere between my lower butt cheek and thigh)." that is the origin of the hamstring muscles, where they attach to the ishium.
It is very common for women to complain of severe hamstring cramps during the sexual act. This usually causes the woman to bring the thigh down, straightening out the hip joint, bringing the knee to the center axis line, until the pain subsides.
As to the click and popping, which is painless, that is also extremely common about the hip. The painless type is usually due to tendons snapping over each other. But, women also have looser hip, due to the hormones they have. So, their actual hip joints can sublux, or move around in the socket even becoming perched, before falling back into the socket. However, this is more of a deep, low, clunk sound and in the majority of patients, painful.
If you are having significant problems with the hip, which is keeping you from enjoying the time with your partner, seek out a good hip surgeon. Do not be embarrassed about this problem. You are by no means alone, this is a common complaint heard by orthopedic surgeons.
Good luck.