I don't have a particular dog in this fight, but the sentence that would come into play is bolded.
10. Non-Disparagement. Employer agrees that it will not disparage or
encourage or induce others to disparage Employee. For the purposes of this
Agreement, the term “disparage” includes, without limitation, without
limitation, any statement, written or oral, public or private, or engage in any
other actions which disparages or discredits Employee to the press and/or
media, any individual or entity with whom Employee had or has a business
relationship which would adversely affect in any manner his reputation.
Nothing in this paragraph shall preclude Employer from responding truthfully
to a valid subpoena, a request by a governmental agency in connection with
any investigation it is conducting, or as otherwise required by law.
The burden on the plaintiff in the regard to the spouse would be to show they were encouraged or induced. Following on from there, doing something like speaking to the media or posting on a message board could be a violation.
EDIT TO ADD:
Having now read the whole document, I smell a settlement coming. And removing him from the Website rosters for teams he coached, while leaving other coaches on their rosters after they were terminated... yeah, that was really stupid.