When I was a young mom with small children and was looking for home defense options, I chose a semi-automatic handgun. It was the safest way for me to keep the gun securely out of the kids' hands while making it possible for me to get it quickly. It also cost me the least for accessories and necessities (such as ammunition and storage methods).
The sexist idea that women can't rack a slide should have died a long time ago. After spending ten years working at a professional firearms training school, I have still never met a healthy adult woman who could not be taught to rack a slide. It usually takes less than five minutes, which means it doesn't exactly require a high commitment to training. It just takes someone who knows what they're doing to teach the easiest way to do it.
Revolvers are difficult to master for defensive use. If there's any question at all about her hand strength, that should immediately rule out a revolver because of the long, heavy DA trigger pull. (Lots of reasons not to use revolver in SA mode for self-defense -- safety and speed the most important of those.)
So for those reasons, I chose a semi-auto handgun when I was in that same situation. In retrospect, it was also a good choice for me because it really minimized the learning curve; when I was ready to carry outside the home, I did not need to learn a different weapon system. Handguns make good self defense tools because they are easiest to work with in tight quarters (think hallways) and -- for a mom with kids, this one's a dealmaker -- because they let you run them with one hand. That leaves your other hand free to push your child out of the way of the danger.
Personally, I opted not to go with a long gun because they're harder to store out of sight. When my kids were small, I had nightmares about a bad guy coming into the main room of the house, and me needing to retreat into my bedroom to unlock the safe to get a gun -- leaving the kids with the bad guy in the main room. Uh uh, no way, no how, in no universe could I imagine leaving my babies with a bad guy. Wasn't going to happen. So I chose a concealable pistol and carried it at home -- locking it up with me in my room at night so the kids would never have an opportunity to get to it and so that I could always get to it immediately no matter where I was or what I was doing.
If she's not at that point in her personal journey (and it's okay if she's not), she may opt for the long gun instead. My own preference in that case would be on the shotgun side, a "youth" model with a short stock, semi-auto 20 gauge. I prefer the 20 gauge because it's a lot less shockwavy to practice with, and because it's less overwhelming in an enclosed space. I choose a semi-auto because it takes a certain amount of training to remember to pump the pump action shotgun, and we know that home invasions most often involve more than one intruder. However, the financial realities might preclude her going with this choice. If she ends with a pump shotgun, she may have to get more training than she really intends to get.
Practically speaking, an adjustable-stock AR in .223 makes a fine home defense weapon. However, the political and financial realities rule that out for her in her situation.
Now, with all that said, if she's not willing to learn how to use the gun safely and well, and if she's not interested in learning the legal and practical realities of defensive firearm use, and if she won't wade through some of the moral and ethical implications of using deadly force to protect herself and her family ... well, a gun isn't the solution to the problem she's facing anyway. To quote the great John Farnam, "Just as cars that 'drive themselves' are currently unavailable, guns that are effective in the hands of the untrained and willfully incompetent exist only in the minds of the naive."
You cannot go to the gun store to buy a substitute for the hard work of learning how to defend your own life.
My personal website: Cornered Cat