No action "fixes everything." What if there's an attractive person at her next job? You'll just get jealous all over again.
You need to deal with your jealousy problem. Jealousy is almost always about insecurity. Is she giving you reasons to feel insecure, other than not giving up this job? You haven't mentioned any. Does she talk about the ex a lot, or spend more time with that person (other than work hours) than with you? Does she compare the two of you? If not, stop worrying. Keep in mind that she has chosen to be with you, not the other person.
If you keep pushing her to quit, you're very likely to drive her away from you.