For situation #1:
The best route is straight down the hallway; that maximizes distance and your visual. The tricky (read dangerous) part is all the doors - they are all threat areas. The BG could already be in any one of them.
Since the guest bedroom door is closed, that helps.With it closed a BG can't see you without opening it; if it opens it'll be a cue.
If you really believe there's a imminent threat you have to 'clear' both of the children's rooms. The doorways and closets are all threat areas, in fact anything you can't see through, around, over, or under is a threat area.
Assuming you have your children, you now face 'clearing' your way back to the master BR. If your wife has been watching the hallway, she can tell you if it's still clear, without her, you could not assume that because it was clear on the way to the kids, it is still clear.
Plus, if a BG appeared behind you and the kids, the wife is armed, the BG may be, you, your kids, and your wife are all in a line with the BG - very, very bad.
As for situation #2:
Assuming your children are not upstairs, don't go. I know we don't want to call the police, but clearing a house is very, very dangerous, even moreso if you are alone. First, stairways are especially menacing and dangerous. Then when you get to the top of the stairs you basically have a four way intersection and there is no way one man can clear this configuration without turning your back to an uncleared area. If you make one mistake it could be your last.
Based on a bunch of FOF scenario training I've had, your house is a nightmare for one person to clear, and don't feel bad, most all houses are nightmares for one person to clear. I've even had two opportunities to clear a house with the local LEO. One was frightening because of poor tactics on the part of the officer, the next time two cops and I went in and that didn't seem so bad - they had much better tactics.
Call the cops, let a bunch of them check it out.