This problem is unfortunately very common. I started lurking around here a few months ago because I was experiencing the same thing. It seems like somebody asks this sort of question at least once a week. I’ve been reading up and trying all kind of stuff, and I feel like I’ve been making a little progress lately.
Larry, it seems like you have the problem pretty well identified. The muscles on the outside of you right hip/thigh aren’t working correctly, so the muscles on the inside are having to work overtime. When ever you move, even when you walk, your body is shifting the work to the muscles on the inside of your right leg, and the outside muscles on the outside of your left.
You mention doing the Agile 8. I tried this warmup for a few weeks myself, but it didn’t seem to help. I think maybe the moves are just a little too advanced. The routine is great to put your hips through a good range of motion, the moves are too “Big.” Rather than fire up my glutes, I think I just cheated my way through the motions, using my lower back and hamstrings.
I came across this more regressed glute warmup somewhere on this forum, and I’ve been trying to repeat it as often as possible;
Clam Shells
Glute Bridges
Seated Psoas Hold
They are really easy moves, where I can really focus on one area at a time. The clam shell especially good. Try it, and see if you can “wake up” the outside of your right leg/hip.
Another move you might try is the Peterson Step Up. You’re on the right track with the Bulgarian Split squats and other single leg work, but you said yourself that the split squat doesn’t feel right. I think it may just be a little too much right now. The Peterson Step Up is a one leg move, with a short range of motion. I think it’s usually thought of as a move for the knee, but I can really feel it in on the outside of my hips too. After a few sessions, I could feel my right hip again, and flex those muscles to square up my pelvis. After a few weeks, I can do bodyweight lunges on my right leg without falling over or any discomfort. Soon, I’m hoping to add some weight, then progress on to the Split Squats, and then front squats.
You could also try some of the half kneeling exercises from here;
Here’s a guy having the same problem
This is pretty long and rambling, so to sum up;
Clam Shells
Glute Bridges
Seated Psoas Hold
as often as possible to fire up your hips and glutes and try to get you “lined up” properly.
Peterson Step Ups a couple times a week as a gym lift. Once you get good at them, try some harder stuff.