How you respond to such a threat is going to depend upon a lot of specific variables that would be hard to know or account for in this particular post. For example, in my home we currently have no children, and all of our bedrooms are located in the same basic area of the house. From my bedroom door I could effectively control movement throughout the upstairs level of the house, preventing an attacker from advancing on my position, or transitioning from one area of the house to another. If I had children in the home I'd probably leave them in their rooms. The other bedrooms are on either side of the master bedroom, and the line of fire from the door of the master is away from those bedrooms. Again, someone would have to advance on my position to take any of the bedrooms, and I would have an effective ambush position if that were to occur.
But, a home invasion wouldn't necessarily occur in that manner. What if your bedrooms are on opposite ends of the house? Many homes place the master and secondary bedrooms across the main floor from each other, and you could find yourself in a position where a criminal is between you and your children. Or, what if a break-in happens while you aren't in your bedroom, or your children aren't in their bedrooms? What if you're in the shower, or your basement, or anything else? Simply put, a one-size-fits-all solution does not exist to these tactical scenarios.
Honestly, there are times when going to the threat is going to be the right thing to do. Make no mistake about this, it's a very dangerous thing to do, but it could prove necessary to protect your family depending on your circumstances. Needless to say, it's always preferable to do the ambushing, rather than being ambushed, so you should carefully consider the critical need to conduct a search before doing so!
I disagree with the idea that it takes four armed guys to clear a residence safely. We routinely find ourselves in such situations at work, and we often conduct clearances with 2 officers on routine patrol. Obviously more is better in these cases, but two can certainly get it done with most homes in a pinch. But, it's important to keep in mind that when I clear a home with one other officer I'm usually doing so in situations where we don't know if there is a threat in the home or not. And, we're well trained for these kinds of clearances. If we have an armed barricaded subject, we're going in with a SWAT team, probably some gas, some flash bangs, a police dog, etc.
As for the linked video above, I kind of laughed at that hypothetical, as it doesn't represent 99.9% of the cases that would be considered a home invasion. To have 3+ attackers armed with rifles moving throughout your house using any form of tactics is going to be extremely unlikely, unless you're facing down a SWAT team (in which case you better just do as you're told).
The overwhelming majority of home invasions are conducted by those who have other nefarious intentions (other than just simply killing you): burglaries, robberies, sexual assaults, etc. More often than not the home invader is going to be a burglar who may or may not be armed, but probably wasn't expecting to find a homeowner inside. A violent robbery can certainly be a realistic threat, and may involve multiple attackers, but I've yet to see one where three guys armed with rifles invaded a home together. In the area where I currently patrol the most common "home invasion" is actually drunken college students kicking their way into the wrong house after they discover that the key to "their" door doesn't work.
All bets are off if you're a drug dealer, or otherwise involved in some type of organized criminal enterprise… those are the situations where I've seen the most violent home invasions in the past.