1. Is what not “yiddish”? giving her the ride? or not giving her the ride?
2. perhaps keeping conversation to a minimum (or none at all)
3. Why would you need to quit your job because you’re not giving her a ride? as you said “The frumkeit at work is proper”
4. not sure of the relevance. either it’s OK to give her the ride or it’s not.
the answers to these questions would likely vary widely depending on the community you live in, and to some extent your personal hashkafos (and also to some extent your wife’s opinion – which you stated)
this should be discussed with your own personal rav or rosh yeshiva who knows you.
by asking here, you will not get any clarity. you will be castigated as a parutz by some for even considering giving her the ride. And you will be ridiculed by others for using frumkeit to not help another jew.