The above advice about 'a plan' is right on target.
What you really need is some 'delay' in your home defense planning, so that you are not initially aware that your perimeter is breached when someone is climbing up the stairs.
Given sufficient advance warning, the answer is (as stated above) "move to a position where you can defend the kids (put the kids to your back), and then hold that position with a cell phone in your hand dialed to 911."
There are many ways to engineer an internal position from which to defend the kids - one of the easiest is to install a solid core door with security hinges and a deadbolt in the kid's bedroom doorframe. Move both kids into that room, and lock the door.
Too many other options to list, home defense planning can get complex - but the point is that to have any workable defense the goal is to recognize that you're under attack early enough that you still have time in which to respond. Dogs can buy you that early warning, or alarm systems can also perform that function (or both), but one or the other should be a part of your home defense planning to allow you to take necessary steps to respond appropriately.
Treat everyone you meet with dignity and respect....but have a plan to kill them just in case.