Recently sold home after 23 months with large capital gains. Do I apply for the work-related move capital gains exemption based on the details below?

Because it is not new employment, it probably does not apply.  I could see an argument that she is taking new jobs and your move would be closer to her work locations but it is not a "new job".

You meet the requirements for a partial exclusion if any of the following events occurred during your time of ownership and residence in the home:

1. You took or were transferred to a new job in a work location at least 50 miles farther from the home than your old work location. For example, your old work location was 15 miles from the home and your new work location is 65 miles from the home.
2. You had no previous work location and you began a new job at least 50 miles from the home.
3. Either of the above is true of your spouse, a co-owner of the home, or anyone else for whom the home was his or her residence.