Get Your Dog Care Questions Answered by Experts
What breed is he?
Approximately how old is he in months? ballpark?
Does he swing with the back leg or the front?
The reason I ask is the carpus and radius are in the front but you mention a gait issues in the rear.
Any other history will be helpful.
Well, this gait in a toy breed dog can be a result of a few things. First, if there is an angular limb deformity in the front, this can alter gait in the rear. However, there are some developmental issues common in toy breed that must be considered. First, a luxating patella (kneecap pops out) comes to mind. In some cases, the knee cap is never in place. This can lead to changes in bone shape in the femur and tibia which can alter gait. Surgery can be a rewarding option in some cases to ensure the patella stays in place.
Also, the is a hip issue common to toy breeds called Legg-calve-perthes disease (aka avascular necrosis of the femoral head). Getting the jargon out of the way, this is essential the fast degeneration of the ball of the hip joint because the artery that feeds it is compromised in some way. This can create a strange gait or limb. Surgery is typically the treatment of choice and is rather rewarding. The procedure is called a femoral head and neck excision or FHO.
If there was a growth plate issue in the front leg, it is also possible in the rear. Keep in mind this is rather rare to see in a front and rear leg. The mild angulation you see in the front is not unusual in a yorkie but can be worsened if the growth plate in the ulna (the other bone next to the radius) is damage from jumping off of something at a young age. This is a much bigger and obvious problem in giant breed dogs because they grow so much more after injury.
I would consider having him looked at by an orthopedic veterinary or at least a general practition with some experience in the field. If xrays have been taken, they can be review by the orthopedist or by a radiologist. Some of these issues can be seen on xrays but the changes can be VERY subtle. I hope this helps and gives you direction.