I have a picture on my phone of my wife shooting an M60, so it's hard for me to "relate" on this subject; but, you've received some good advice here. Like they said, use psychology and make it about your kids... and make darn sure she is VERY well-trained. Make it fun for her to shoot. It probably is for you.
As others have mentioned, having her wear the gun she learns to use is important. It does no good sitting in a closet unloaded, or even loaded for that matter. You have a fraction of a second to react and clear leather in most instances.