My horse did this too: beautiful changes from left to right but huge bucking changes from right to left…he could launch me straight out of the saddle.
It took years to get better. That’s probably not what you want to hear. Only recently has he started to do nice, normal changes both ways. It’s like he suddenly calmed down about changes (he would get quite excited about them).
Hopefully it doesn’t take you as long as it took me!
Thanks for the detailed explanation, cnm161!
I have been traveling to a arena in mirrors so I can really see what’s going on and making sure that I have him straight. Have also tried several of the exercises- seems weaker on his left hind for sure. Not even trying the changes- going to keep at the strengthening exercises for a few weeks and I think I may inject his hocks. I am not usually a fan of just injecting as maintenance, but he is a little older (13) and this is harder work for him. I will keep plugging along and thanks to all for the suggestions- makes me feel like there is hope 
Looking at his hocks is definitely a reasonable idea. I have one horse in particular that loses his changes when his hocks get sore. He doesn’t even feel lame but suddenly can’t do them worth a damn. After I inject his hocks, the changes come right back like there was never a problem. A lameness exam and x-rays might be a good starting point though. There are other hind-end problems that can affect the changes as well. Best of luck!
It is more than fair to have your vet look at his hocks. I would have to agree with those who said to watch your position. There is a lot of jumping around riders do thinking they are “helping” their horses change. I have found that when you are training a horse new to changes, still use small aids like you would on a schooled horse. A buck is a strong reaction to the change aid, so think even smaller than what you are currently using. Also, I have noticed that riders can move their outside leg too far back thinking that will help. It can just puss them off! Again, smaller aid. You must really be sure you are giving the new inside rein toward their mouth. If not, you can construct them, they can not be able to change, or get frustrated that there is no where for them to go.
My gelding would try to stick his croup up when he was learning the changes, but my mare did a little bucking, but I was over aiding and humping around like a fool. This past weekend we got 2 8’s for the changes in 3rd level, so it does pass if you remain calm and continue to make little aids!
