Welcome to Calguns!
As NorCal and 9MM mentioned, start slowly and practice, practice, practice!
On the topic of kids, I am the Mean Mom and very strict when it comes to firearms training for my kids. I've raised six in my time -- two girls and four boys. With the exception of the younger boys, we've shot as a team in various pistol competitions.
To prevent bad habits and to allow for understanding of the sight picture, I agree that shooting Air is great and inexpensive. I laughed when I was first approached by the match directer at Chabot; he suggested I take up Air -- after all, it is an Olympic event. It really helped me with my follow-through and trigger squeeze. It has carried me through to the slow fire stage of .45 and learning to control the recoil while maintaining the sight picture. Shooting offhand is not as easy as it sounds.
If my kids could demonstrate the patience and discipline for Air, I gradually moved them up to live fire with a .22 target pistol. My girls were better focused, while the boys had better arm strength. It all worked out -- safely -- which is my No. 1 Priority.
I understand your anxiety, so don't feel bad. Our babies are our most valued treasures, so we need to be vigilant about instructing them correctly.
Best of luck to you!