Dogs who have trouble with a rear leg (especially when they do that hopping thing after coming up lame during a run) are classic cases of CCL injuries.
The CCL (Cranial Cruciate Ligament...the dog's version of the ACL) runs on the outside of both back legs. It connects the upper bone with the lower ones, and has a nasty habit of breaking.
Unfortunately, the only way to diagnose this is with a trip to the vet. Your regular vet should have taken x-rays and palpated the limbs to look for hallmarks of the torn ligament (legs with a ruptured or damaged CCL show a 'drawer' movement..which means the bones slide side to side, whereas an intact ligament doesn't allow for that sort of movement).
If it turns out that the problem is a damaged CCL, the only way to repair it is surgically, with either a TPLO (which is a procedure that involved breaking the bones and applying a plate to hold things together) or with a lateral suture (where essentially high-test fishing line is used to replace the broXXXXX XXXXXgaments). The TPLO is more expensive, but works great for active dogs who have the potential to reinjure the limb.
I hope this helps.