Personally, my mobility in the hips and shoulders was the worst when the muscles of my hips and back were weakest. My body just didn't want to move into some positions, because the muscles it took to get there were weak. My body would find ways to "cheat" to cover for the weakest muscles, and the result was moving really badly. So if I did something complicated like shuttle runs or cariocas, I would just move through them in the worst way, and not get much out of them.
For me, the most "useful" or "productive" part of the shuttle run would be that deep sideways lunge and rapid change of direction. The best part of cariocas is keeping the spine neutral, and upper body in position while the hips swivel and shimmy.
So I just made an effort to focus on those "pieces," and "activating" the muscles involved in them. I tried the Agile 8 and Agile 11, but I had the same problem. The moves were too much. The "groiners" or "mountain climbers" especially. My hips weren't ready, so I cheated my way through, and actually did the reverse of what I was trying to accomplish.
I had to regress that stuff all the way to clam shells, seated Psoas holds, hip hikes, and Peterson Step Ups. By doing easy stuff I was able to get those lagging muscles going. I still do the same moves, but now I use bands and dumbbells for resistance.
I thought I would need explosive, low to high, dynamic rotational moves like I was a track and field guy. What I've really been doing is anti-rotational stuff. 1 arm farmer's walk and sidebends. Pallof Presses in the half kneeling position. Step ups on the right leg, with a dumbbell in the left hand. Lunges and 1 Leg Calf raises, loaded the same way. At first I would twist and lean and fall all over the place doing these. As I got better at this boring junk, my hips became more stable, everything else got better too. With my pelvis under control I got a lot more out of hamstring and oblique work.
1 arm kettlebell swings alternated with standing leg raises are good for this. Really hinging, and feeling the hamstring on the swing. And feeling the off leg drive, and "twist the foot into the ground" with the off hip on the leg raise.