I'm a "bad" mom because I choose to spend more time with my dogs than I do with my almost adult teenagers. They don't want me around anyway!
My daughter use to go to training with me, she enjoyed it...until she hit 15, then it was stupid/boring.
I don't know how the balance can work with kids/dogs/training, unless the kids are interested and want to be involved. Otherwise you do have to put the kids first, dogs last. And kids in sports(travel ball/hockey/martial arts) is full recreational time. It is a huge commitment financially and time-wise. Just like dog training, if you are competitive, same thing.