"stranger bangs on the door" types of ideas is a larger issue than firearms training.
You've got a lot of other components that wrap around that, and maybe look at "low hanging fruit" or simple components to the overall solution before tackling firearms training:
1) A quality locking storm door with some visibilty that also allows the inhabitant to talk to someone outside without completely opening a passage into your house
2) An intercom system w/video
3) A chain on a quality security front door
4) A large dog - especially gaurd dog type breeds
5) Electronic alarm and alerting system
The issue of getting trained with a handgun is on the list somewhere but it doesn't prevent or preclude these other things from being addressed. And since you and your wife seem to have some fairly significant obstacles to her getting training right now, I wouldn't take an all or nothing approach to it and do nothing until she can get trained. There are other things that can be done as early as this weekend.