I have a similar family situation; when my twins were born (boy-girl) we already had a 2 year old daughter and a 1 year old daughter.
When they had reached the age of your kids, I had them watch, over and over, the NRA Eddie Eagle safety video (still available from the NRA) which taught them when they saw a gun, they were to: stop, don't touch, leave the area, tell an adult.
My "kids" are now in their 20's going through college and graduate school, and they are all home for this Easter - I just quizzed them about the video, and 15 or so years later, they can still repeat the Eddie Eagle mantra.
My wife is petite, small-statured, around a 100 or so lbs soaking wet, and also did not (and does not) love to shoot, but she learned to do so after we had someone try to break into our home when I was out of town and she was alone with the kids. She called 911, but as the saying goes, when you need help now and the time is measured in seconds, the police are only minutes away.
After shooting lots of pistols, rifles, and shotguns, we agreed on two options for her: a K-frame 38 with factory wadcutters, which was low recoil but as much as she could or desired to handle. The pistol was and is kept in a gun safe bolted to the closet wall where you push in a combination and the door pops open.
The second choice is a Rem 870 youth model in 20 gauge, loaded with #4 birdshot, chamber empty, safety on, and was kept on a shelf out of reach of the kids.
Good luck. And by the way, if you want your kids to go to college, start saving now, but no matter how much you put away, you still won't have enough $$$$........