my wife enjoys shooting handguns. she doesn't care for rifles and definitely does not like the shotgun. but she absolutely loves pistol caliber carbines. her favorite gun is a hi-point 9mm carbine and other is the lever action shooting 38spl. they put a smile on her face every time and she enjoys it way more than pistol shooting. a hi-point carbine is around 300$, is extremely reliable and gives that little 9mm round considerable more punch. it's pretty quiet as guns go, and would be better for indoor use than a pistol or shotgun in that respect. the best thing is its cheap enough to whereas you wouldn't have to part with your shotgun, plus if you doll it up pretty, the girls will love it. I am in the process of building her an AR pistol in 9mm ATM, I think she will also like that. something to consider anyways
here's her gun, a few bucks with of krylon has held up nice for the last two years so far
but to your specific question, would I trade a shotgun for a pistol for HD? yes...I would. when I first got into guns, I just bought as many as I could, thinking one was better than the last. for a good period of time, I kept a 12ga h&r pump in my bedroom for HD. it wasn't until I started getting serious about practicing tactics and scenarios that I realized the shotgun was probably the worst option of my collection for hd. there was no way to maneuver from my bedroom into the tight hallway that leads to the kitchen on one side with French doors and the living room on the other with the front door without giving up cover from either front or back. I really wanted the lever-gun to fit the role due to its quietness and powder, but it to was slightly too long and I couldn't take targets nearly as fast as with my pistol. my ar15 gave the same issues, but was better at acquiring and taking fast target, but is extremely loud. in the end I built a 8" 300BLK pistol w/o brace and it has proven to be the best defense for my homes layout, and being somewhat quieter helps too. the shotgun has been locked in safe for a long time. but if all I had was a shotgun or my full-size 9mm pistol, I would have to take the pistol. I can acquire it and have it ready in my hands, safety off, pointed in mere seconds with one hand w/o getting out of bed even. unless I had a short barreled shotgun, that would be impossible. power of the gun, I think, I blown way out of perspective. I think the tactics need to come first, and as a shotgun would make a great gun if you had fair warning, you will likely not and that is where small and compact is necessary. you need to run some drills/scenarios of multiple attackers in your home and see how it fits your situation. but I would bet a pistol would be a better tool for most people.
pistol/rifle platform. best for MY home situation. small enough to acquire quickly and transition from hallways and tight spaces, powerful enough to take care of business