Why do you consider your DGD to be in such danger that you want her to do such classes?
I can understand you offering her a chance to do these classes, especially as she can do them with an uncle, but why worry if she turns the opportunity down. Would you be bothered if she turned down a gymnastic class?
When DS was about 8 I encouraged him to do judo, for the same reason you want your DGD to do karate. It was a big mistake. He didn't enjoy the classes, I persevered too long and far from building confidence it undermined the confidence he had.