Maybe she just wanted you to ask her if it was ok to take him shooting. It could be a respect/boundary thing and have little to do with guns. If it was me I would talk to her in a neutral setting. Not at your house or her house and just the two of you. Take her to lunch or get some coffee. Tell her you know that it is her son and it is her decision to make. Don't get defensive or mad. You need to be the voice of reason. Explain that guns were an important part of your upbringing and you want to pass it along to your grandson. Tell her that showing the kid how to use a gun responsibly under supervision will make him less likely to abuse or misuse them. Invite her to come along, so she can see the safety precautions you are using to protect the little guy. The important thing is to make her feel like it is her decision not your decision.
I wish you well. She may not let him go and she might apologize for blowing up and give you her blessing. Hard to say from here behind the keyboard. Don't lose your cool, she is sitting in the catbird seat.
