The article you linked
is interesting and thought provoking. Mr. Harris is correct on many points. However, I think his emphasis on escape trivializes the natural intent of a parent to protect their children. In the event a threat to the children (and/or their parents) materializes the parent(s) should do as he suggests -- an explosive reaction to protect and defend the children and themselves. But not with the idea of escape, but of vanquishing the threat entirely.
You mentioned obtaining a Beretta pistol. Hopefully that is a major caliber (9mm or .40 S&W) and not a pocket pistol like the .380 or smaller. Most of the Beretta pistols are good choices. It could be beneficial to familiarize your wife with the function of the pistol - how to load/unload, operate the safety, use of the hammer, squeeze the trigger, etc. Doing so with a handful of snap caps will give her the basic concepts.
If you want to worry about stoppages, I suggest you both
watch Thunder Ranch's Clint Smith
demonstrate clearing a stoppage on YouTube. Then use an empty case with snap caps to ensure the lesson is understood.
Remind your wife that if someone is trying to break in or succeeds in breaking in, there is a real and imminent threat to her children. There is no need to be polite. No reason to "play fair". She should believe that said intruder(s) are there to eat her children like vicious animals because the outcome could be the same. If they seriously injure her or kill her, they can kill her children or the children die from neglect if you're not coming home that night. Worse, they could take the kids leaving you forever wondering if they are still out there. Tell your wife the Beretta has 15 rounds (10 in some states) and if she has to use it, use as many shots as it takes. Ammo is cheap, lives aren't. Holes in walls and appliances can be fixed a lot easier and cheaper than damage to your family.
Having an intercom at the front door will allow her to answer someone at the door while safely in the house. Ask friends and neighbors to phone before dropping by as a courtesy (if she's put the twins down for a nap she may want to rest then too). Any unexpected person at the door gets to talk over the intercom.
Over the intercom, someone claiming to be with UPS, Fed-Ex, Airborne, etc. can be told to leave the package on the step. Before opening the door for a "signature required" package, visually check from a window. They should be in uniform and have a company truck parked out front. If not both, then phone police. Similar rules apply to utility personnel. They can wait while she phones the police to check them out or calls to verify with their company. Even if you lack the intercom, this can be done through the door.
This may sound like paranoia to her, but assure her it is not. It's the safety of her children that come first. Anything happens to her, it affects the children too. She's a busy mom with twins so service people can wait.