Okay, there are a lot of stuff going on here that can be dealt with in so many different ways.
I believe the ultimate question here is not "what would you do if someone had a gun to your child's head" but rather "is your family better served with you making a grand entrance or waiting for authorities to arrive on scene?"
Let's think about this step by step...
This is the scenario, right before leaving work, you put your carry piece on, you arrive home to find that even though the door is closed, there are obvious signs that the door was forced open.
First thing's first... call 911. This should be a given.
Step 2: Check to see if my husband's car is in the driveway. HOWEVER, just because my husband's car is in the driveway does not mean that he is still in the house with the kids.
Step 3: Call the home phone and/or my husband's cell phone. If there is an answer we go from there.
Step 4: Try to gain intel from OUTSIDE of the residence. As I said before, there is absolutely NO reason to believe that there is anyone in the home at this moment. My husband could have gotten the kids out and gone to a neighbors house to call 911 and is there waiting. Yeah, it would be unusual for him not to call me, too, but why give a bad guy a hostage or walk into a situation without more information.
Yes, about now I would probably be drawing my firearm but I would still not make entry. I would circle the house looking for other clues that an individual is either still in the home or has left. If there's a strange vehicle parked on the street with someone sitting in the driver's seat and the engine running, then, yeah, there's probably still someone in the house. Is there a car? How did the individual get there? Can you take down a vehicle description? First, you don't know that anyone is in the house, much less where they are.
Got a good pair of binoculars in the garage or the car you can use to try to get a peek into windows? You should! What can you see?
You know your house.. going in and getting yourself into trouble means that you can't give responding officers the layout of your home. They are going in blind. You staying outside could mean a more successful response because you can give responders the layout and potential strengths and weaknesses.
But, let's say it's just getting to you too bad and you decide to go in.
When you get to the bedroom, the door is closed & locked. After knocking, or calling out loud to see if everything is alright, there is still no sound except for a low whimper.
Okay, well, I hope you've been at least smart about it until now. In our home the doors have key locks. We have the keys stashed. No need to break down doors.
Anyway, finding an area in the home to stage at would be ideal. Stage in that area and wait, either for an indication of what is going on or authorities. No one is going to be completely silent for very long... especially if there are children involved. Children are likely going to be crying.
Call out from the staging area. If you don't get an answer you can assume that either a) no one is in the home b) the individuals are unable to respond either through intimidation or injury or c) everyone is dead.
It's a tough call but in order not to be a victim yourself you still need to be smart about it. If you have any home clearing training you can proceed in that manner. If you have no home clearing training you should stay out. Seriously!! You should go back out. Of course that's harder said than done when you're family is on the line.
However, if you choose to proceed it should be done carefully. Having done room clearing going to that bedroom door would be a delicate process. It would be likely that officers would have arrived by this time.
Both fortunately and unfortunately our bedroom is designed very well to be hard to access. Sneaking up on it would be hard and dangerous. Good if you are the good guy held up. Bad if you think your family is in there and want to get to them.
Now that I'm finally to the bedroom door I'm going to listen. Listen for possible position. Left of right side of the room. It will make a difference in which side of the hall I hug if/when I decide to try to make entrance. Again, I have a key so there's no need to break down the door but the door could be barricaded. I call out again and there's nothing.
Again, what evidence do I have that someone is still in the home? Any evidence to suggest the individual has left? If I have reason to believe that the individual is gone I may make entry. If I have reason to believe he's still there (an unfamiliar voice, a vehicle still on the street or in the driveway, etc) I might be more cautious.
There's a whimper in the bedroom... is there any other access point? A window perhaps or another door? An a-joining closet? Is there some way to enter or gain a vantage point that would not be expected?
If I'm thinking rationally (which, I admit could be VERY hard in this situation) I might choose to back off at this moment. I might choose to make entry.
Again, depending on what side of the room I think he is at will make a difference in which side of the hallway I hug. I don't want to be stuck in a fatal funnel. I don't want to give myself away right away either. I can unlock the door, open it and retreat to cover and try to pie the room.
What about my family.. Does my spouse (my husband in this case) seem injured. Is there a way he could gain an advantage by my being there? Is each child accounted for? Do they seem injured?
He's got a gun to my daughter's head... wow.. yeah.. that would stink.
If I'm doing my room clearing correctly I should be mostly concealed or under cover and be utilizing my space correctly. I might even have a pretty optimal shot without having to do any negotiation or without even being seen or made any demands of. If you don't think that is possible then you haven't seen what I've seen (PS.. JD is really good at this).
I've been to trainings where you are required to do room clearing AND deal with hostages. You would be AMAZED at how many people shoot the hostage. It's scary. GOOD shooters who get caught up in the moment and pull their shots or shoot for center mass which just so happens to be the hostage.
I am proud to say I have yet to shoot the hostage. However, there has been at least once where I felt I could not make the shot and had to give it over to someone else at that distance. Depending on the distance I may or may not feel confident making that shot. I would be loath, however, to put myself into the room.
If I can see that everyone is safe I'm going to stay out of the room. I might try to create a distraction with conversation so that my husband might act.
From there it depends a lot on distance, conversation, well-being of my family, etc. If already injured, all bets are off. I see no reason to believe that someone who has injured a man or children to be hesitant to do further harm. They need medical attention and that means making the scene safe any way way I can.