Lanesd9ve,
Well, if she stands by her decision that a shotgun (in your case, the 870) is out of the question (even though it's a shame, and even though it may only be for now) there are still many other guns she could use.
As another member mentioned above, a semi-auto .22LR rifle/carbine like the Ruger 10-22 is plenty lethal, not just for kids defending the home, or women intimidated by recoil of larger calibers, but for use by us MEN, too. For specific example, MY 22 semi-auto rifle of choice is a Marlin M60 (the OTHER of the 2 top 22LR semi-auto rifles available for DECADES now): 18 rds in the tube (probably CCI's Velocitors), hardly ANY recoil, and EASY to make a head shot with. As many times as necessary. And a .22LR definitely WILL go through someone head (avoid glancing angle/shots of course)...maybe won't come OUT, but WILL go in. That's fine as it's all you need. I don't know ANYONE who wants to get shot, even with a .22LR. And not MULTIPLE TIMES with one, either! In their head or elsewhere. ;-)
I also have a stainless-steel Ruger Mk-III bull-barrel 22LR pistol: THAT is easy to shoot and hit with, too...so a pistol she can carry AND easily shoot is a good possible choice.
As for getting your GF onboard for home/self-defense, tell her you're a TEAM (a "fire team" if you will) and should think/act like a Team. And as such, you need to support each other, so you BOTH need to carry. And as you stated EVEN CARRY @ HOME. For all the reasons we here know. I hope she's not waiting to be a victim before she wises up. Or, see you get hurt (or worse) because she didn't (could not/would not) help out in a time of crisis. IMO, if someone gets hurt because of his/her choice, they reap what they sow. But if his/her choice gets someone ELSE hurt, that's something else entirely.
A horse of a different color. -- the Wizard of Oz
Besides, some years back I recall reading about one incident in a big city: A guy and his gal were out on the town, some street trash tried to mug them (and maybe do worse to HER -- or him...you never know nowadays, with everyone "embracing diversity" and all that crap), and the guy FORGOT his gun (SHAME: Never leave home without it!) -- but she had HERS on her. Saved BOTH their behinds. He'll probably never live that down -- but serves him right for not having HIS gun on him! What if SHE didn't? Don't even want to think about what COULD have happened...and I wasn't even there! ;-)
Remember: Anyone can die at any time. -- Joe Bob Briggs.
...and anything can happen anywhere -- there are no 100% "safe" places nowadays.
Good luck...
P.S. When at home, MOST of the time a gun is ON me (a .32 ACP Beretta Tomcat (inox) in my jeans "coin" pocket is my lounging-around-at-home gun...lightweight, easy to carry yet still a great close-up gun). And I answer the door with it ON me. When taking a bath/shower, it's right there with me but (of course) not getting water on it (even though it's inox). And I double-lock my door so the noise of breaking-in will alert me. At all times a gun is ON me or within arm's reach. No excuses! Ever.
No...we're not paranoid, just prudent.
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Okay...looked at your pic of your 870 again. It goes to prove the old adage that a picture is worth 1000 words. Yes, it looks pretty scary to me, also! I get where your GF is coming from!!
Okay, please disregard everything I posted in this thread about shotguns, like it never happened.
[just kidding]