Just adding to the statistic here for you.
I was around 10 or 11, .22lr rifles at a local outdoor range in a rural area. I got my first pellet air pistol at around the same time as well for Christmas. Dad was proud, mom was livid but learned to relax after she saw that I was responsible with it
To be honest, in order to ensure your kids are comfortable around guns you need your wife to be on board. Sell your wife on the gun idea by using the safety argument (which your kid brought up as well). If there is one thing timid people are more afraid of than guns, it is to be victimized without the ability to do anything about it, especially by another person with a gun. A lot of people who have strong feelings about guns will be the first to go out and buy one right after being mugged.
Tell her that since there is a gun in the house already, she needs to know how it works mechanically so she can operate it in an emergency or avoid an accident. What if you are incapacitated and the weapon needs to be cleared and locked away, or more seriously used against an intruder? This would be a mature and responsible argument. Schedule a safety class for her and yourself at a local gun club or range with a certified instructor. Certified instructors are used to people like her and will convince her in no time that she has to shoot the gun in order to understand how it works. I will bet you this is the magic moment where her attitude will change, at least somewhat.
This approach cured my hoplophobic wife, who until recently proclaimed that she would never even touch a gun. Turns out she is a pretty good shot
One more thing. I really don't like talking politics online, but when it comes to responsible firearms ownership, the two are inseparable. If you value your right to protect yourself and your family, you should also be a member of one or more gun rights advocacy groups. Especially if your listed location is correct.