I'm not legalizit, but I may be able to help. I'm getting over a really bad bout of achilles tendonities (~18 months) which is due to hip issues.
My PT had me do about 20 different hip strengthening exercises. Many work on balance. Here are some:
1. Stand on one leg, balancing.
2. Stand on one leg, balancing, with eyes closed (hard!)
3. Stand one legged on pillow, with eyes open (or closed)
4. Stand on one leg (with or without pillow), throw ball against the wall and catch it. Keep eyes open :)
5. Bridging. Should be something online on this, basically lay on floor and raise your hips up and down, hold, etc.
6. One legged squats. Balance on one leg, while doing squats. Try it with eyes closed! Try it while standing on a pillow!
7. Lunges...you should know how to do these.
etc...etc...etc...
Tex