If it were my kids, I'd limit their training to maybe learning some basic self-defense skills safely at the most. I'd be extremely cautious with a daughter.
Any extensive martial arts training comes with some fairly serious risks and I just wouldn't want to subject my children to it and I don't to the dismay of those who know my background. I've seen kids(usually teenagers) experience some pretty bad injuries in karate, wrestling, judo and BJJ over the years that will negatively affect them for the rest of their lives. I imagine many resent their parents for not doing a better job of looking out for them.
I can't see grappling really being much safer than striking systems in general, just different risks and none of them good, but it all depends on the specific program.
You have to think long term regardless.
https://www.bjjee.com/articles/long-...tion-training/