I don't think the Titans org gave a single iota of care what Vrabel was doing to his marriage, if they even knew.
Only reason they'd care is if they thought it was contributing to losses due to focus, ability for him to coach, or a security risk of him spilling info to her and her giving other teams that info.
And if they knew I'd think they'd try to use it to fire him for cause imo.
The only time a pro team will ever "care" about morals and ethics is as leverage to negotiate contracts. If you're a winner they'll cover stuff up and/or not care.