Uncle has a tough question up; one that there really isn’t a clear answer to.
I have been a shooter for over a decade. My wife has no problems with my hobby and has encouraged me to teach our children both firearm safety and how to shoot well. However, I have found no way to get my wife to try sport shooting with me, due to her negative experiences with firearm victims when she worked in an Emergency Room
He doesn’t know how to get around that emotional barrier and get his wife to come shooting with him; which seems to be a source of frustration for the guy who asked Uncle the question. I agree with Tam who says in the comments that not everyone is going to want to be a shooter, and I also agree with Sebastian who points out that part of the reason guys try to get so many people to come shooting with us is because it helps fight back against the overwhelming anti-gun tide out there.
To answer the original question, I would say that the most important thing to do is not push the issue with your wife. If she doesn’t want to go shooting with her, that’s fine; leave the issue alone. Pestering her and constantly trying to get her to the range is certainly not going to make her want to go shooting. The best solution is to keep shooting, keep going with your kids; and eventually if your wife wants to come with you, she will.
To relate a bit from personal experience, I have a friend who saw some action overseas, and for the longest time wanted nothing to do with any firearm that even looked like something he would have carried. That meant M9s, Remington 870 shotguns, and especially AR15 pattern rifles. It took him several years, but he’s just now finally starting to get over the negative emotional relationships he had with those types of firearms.
So don’t push the issue. That’s the key thing is that you’ve got to take it easy with people who are outside the shooting sports, especially those who have an emotional reaction or association with firearms. You’re not going to overcome that emotion by persuasion, the only thing that’s really going to beat it is time. I can’t emphasize that enough, constantly driving the issue will do nothing but turn her or any other prospective shooter off to the shooting sports. Don’t push it, just be patient. She’ll come around when and if she’s ready.