I've vaped for 2 1/2 yrs. Although I have far less crud to cough up since I switched from smoking, vaping has in fact made my asthma -- wheeziness, tightness, etc -- a bit worse. I think it's the moisture content, because I use very little VG -- I vape 85% PG.
My husband says he doesn't smell much of anything from my vape, BUT, he can tell from the smell when I need to dry-burn/re-wick; he says it smells like "burnt shit."
I vape in my parents' house when I visit them; my mom says the same as my husband, no particular smell; my aunt says the same, that what little smell there is, is like a very weak air-freshener -- since most air fresheners are mostly PG, that makes sense. My stepfather, however, sometimes finds the smell rather obnoxious, and once it made him vomit. I know that when *I* am not feeling well, I don't care for the smell too much myself, it makes me feel a little sick, so I can somewhat understand.
I guess the main thing to keep in mind is, everyone is going to perceive and respond to vaping in their own way. It *might* be true that she is perceiving whatever she is perceiving because of the negative press about vaping -- the "fake cough" that greet many vapers, just from the sight of vapor, because it looks like smoke. On the other hand... her body may respond to the smell and the actual vapor in a negative fashion. Since none of us is inside her, there's no real way to know, and if she is prejudiced against vaping for whatever reason, then it doesn't even really matter whether it's an actual physical response, or psychosomatic distress -- the fact is, there IS distress, no matter what causes it.
To be a good son, the best thing you could do is take it outdoors; if the weather is very foul, maybe take it to a different room as far from her as you can manage, and close the door. I understand that moving and getting your own place is much easier said than done, and requires planning and careful budgeting; it's a big step, the first time one moves beyond one's parents' home, and shouldn't be taken lightly. But, if you want her to respect your decision to switch to something a lot less harmful than smoking, then you need to respect the fact that it clearly is distressing her to be around it. If you love your mom, you should care about her distress, above and beyond any considerations of respect or "her house, her rules." It's simple kindness, for someone you care about.
Andria