You are absolutely correct in what you have said, . . . but do this.
Get a young person (not one who knows the house), . . . offer him $20 to help you learn how to "clear" your house,
Give him a few minutes to "case the place" then arm yourselves with squirt guns, . . . tell him to go hide and try to "shoot" you without getting shot himself. If the kid has any moxy, . . . you will lose 19 out of 20 times. There are just simply too many places the bg can hide and see you, . . . yet you will not know he is there until you are bleeding.
Yes, . . . safety for your family is why you are there, . . . no argument. There must be some compromise in your own personal safety and your providing safety for mom & the kids, . . . but you getting shot does not help them at all. And all the "stuff" that the bg's can haul off in the 20 minutes it takes for LEO's to arrive are not worth you taking a bullet, . . . or worse, . . . or one of the kids or momma taking a bullet from a wild shot out of one of the firearms going off in the house.
Seriously, . . . I'm not slamming our picking on you, . . . but I really do think you can devise a better plan for protecting your family than trying to clear your house by yourself. Ask any LEO you can find what two things scare them the worst, . . . "domestic disturbance" will be high on their list as well as "live house clearings", . . . and they do both as teams of 2 to 10, . . . never alone.
May God bless,
Dwight