My mare, her transition from the walk always goes to the jog before the extended jog unless I immediately start out posting.
If I am sitting down, relaxed, she will jog. If she goes too fast, half halting and squeezing with your seat, providing some resistance until she slows down works. Then when she does get to the jog you want, relax, loosen your body and hand, and give her the release.
Mine also learn that posting or being just slightly more forward in the saddle means the jog should be extended or picked up to a strong trot, depending on how much I push them. In the western horsemanship class, the extended jog comes from just a tiny forward movement in your hand and body, so if I don't come forward my mare knows we are NOT doing that.
Lots of halt halts and softening should do the trick for you.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.