If I had a family, and there was danger approaching them, I would do whatever I could to get between them and the danger. I will not wait it out while others, especially family, are at risk.
This is a good situation where a decent piece of body armor could come into play. You know you have to leave your secure position. It's a not convenience or choice. You have to leave security in order to save your family. Stack the odds in your favor. A good vest can be had for less than the price of a new gun. And when you're forced to move around in a dangerous area to secure others, it could save your life.
Is switching rooms and option? Have the rest of the family upstairs while you and your weapon are closest to the intruders entry point?
Have you gone over a security plan with the family? Tell them to come upstairs to you a the first sign of danger. Conduct a few drills if you can.
Home invasion deterrence and preparation focuses heavily on time. The more time it takes the BG to get in, the more time you have to get your house in order and the more likely it is he will give up and find an easier target. I'm not sure how many modifications you can make, but a metal door and metal frame with a good deadbolt would be a good start. Add a motion detector light to the porch. If it's a bad neighborhood, a steel cross-bar in the inside of the door or some sort of steel gate could be a help to. Bars on the doors and windows can be unsightly, but that can be managed with a good design and paint job, and they definitely add some great physical security.
I know the feeling about dogs. I just don't like them. I'm not going to rant about them as this is neither a dog forum or a dog thread, but suffice to say, I will not ever be getting a dog. So finding other ways to secure my apartment can be tricky, but doable with enough good advice from places like THR.