Kimio, your dilemma is thought provoking from a couple of perspectives.
One side of me says that an untrained person, male or female, is unprepared to make ALL the decisions necessary before a gun comes into play. When a 3 year old is added to the scenario, with an absence of training or familiarity, well....Sorry, but no firearm at all may be the better choice. If you choose to devote to a self defense plan, you must also commit enough time to make sure your plan is going to have the desired effect.
Two, malfunctions in self defense are not limited to the mechanical side of the firearm only. Mental malfunctions are the result of a lack of training, and a lack of a repetitive, second nature approach to that goal is the thing that nightmares are made of.
Three, you mention a couple of reasons that training is impossible, namely time and money. How about a more pragmatic approach to home security, one that involves hardening the home perimeter, with better window and door locks, motion detecting lighting outside, common sense things that can work with an every day plan of what to do when things go bump in the night, (or the day). Also, what neighbors can be counted on for help in your absences, programming the police phone number into the phone, etc.. Figure out a way to keep the dirtballs outside and you will not have to fight them inside.
I guess I am getting too old to take unnecessary chances, but home defense is way too important to pretend it is not time consuming.
Good luck in your search for an easy solution, friend.