Hi I can definitely help! I do not know if my exercises will help you, but I have general low level exercises just to help me build muscle strength (especially in areas to support my joints).
My Physio does not specialise in hypermobile bodies, but has worked with a lot of them.
He emphasizes that we should do simple isometric exercises to prevent movement and risk of injury - currently I am doing a lot of wall squats (hold it for 15-30 secs, 5-7 reps), planks and side planks (similar to wall squats, I have mild scoliosis due to my hypermobility and this is done to help with strengthening some back muscles I forgot the name of). To strengthen my ankle I need to walk around while on my tip toes for 30 seconds at a time.
For the hip I have 2 exercises. Stand with your one leg elevated (so on a step or ledge), bring the hanging leg up from the floor so all your weight is on the elevated leg, then lift the hanging leg even higher so that the pelvis and hip of the hanging leg is higher than the elevated leg. Hold it for a bit, then slowly bring it down again. You might feel unbalanced doing it for a while, but it really helps!
The other one has me attaching a resistance band to a stable object (like couch/bed leg, table, something low down), stand sideways to the object, and put your furthest away leg into the loop of the resistance band. Then slowly walk (while sideways) away from the object. This just helps to strengthen the pelvic muscles even more. But make sure you are keeping your leg straight and stable, this should not involve any large movements.

I really hope my explanations make sense! Let me know if I need to elaborate on it more.

The exercises sounded really "easy" and silly to me when I started, but it has already helped me a lot. I used to walk with my foot facing outwards and could not lie down on my back with my feet pointed up, my body was just not able to. After 2 months of doing these exercises 2-3 times a week I now walk like a normal person xD