I'll tell you what I'd do.
While your daughter is with you, it is YOUR'S/HER time. Her mother cannot tell you what to do with that time.
With that said, I would take her shooting, and not out of spite. Let this blow over a bit. I would also take along someone with character. That way, if she throws it in your face, you have a credible witness. Hell, video tape the affair so there are no questions about what really happened.
I don't know if the two of you get along, but you could always invite the other side to go along. It sounds like her significant other is interested in shooting as well. I know it may seem odd at first, but many families separate and remain friends with one another. You have to put the whole relationship thing aside and just be cordial. Not only will your daughter see that mommy and daddy can get along, but can enjoy time together with her without any animosity.
Buy her a .22, let her pick it out, and make her a responsible owner. She will learn about it, clean it, and lock it up. Read the 10 commandments and you can even make a game out of quizing her with them. BTW...
EPIC FAIL