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Answer for Anger Management

Technically, yes, if you do it in good faith, with an aim to help the employee and for a justifiable reason that you can document.
The risk is that forcing an employee to take anger management may be seen as a harassment tactic and a means of humiliating the employee. After all, anger management is a sensitive subject. “You need anger management” has become a popular insult among road ragers and such.
Also keep in mind that if the employee belongs to a protected class under human rights laws, requiring anger management could get you sued for discrimination. A couple of years back, we discussed recent court cases in which an African-Canadian employee required by his employer to take anger management claimed he was the victim of racial discrimination and stereotyping. I believe the cases were split 50/50 on whether the claim had merit. (One bit of good news is that courts have made it clear that anger issues aren’t a “disability” requiring accommodation  See https://hrinsider.ca/not-discrimination-to-fire-employee-with-anger-management-issues/ )
From the payment Q, I take it your organization doesn’t offer anger management under an EAP or mental health plan. Even so, employers often do offer to pay for anger management, especially for a valued employee they want to help. But unless there’s something saying otherwise in the employment agreement, collective agreement or terms of an employee benefits plan, you probably don’t have to pay for anger management services.
Great Q and I hope this helps. Glenn