I'm no attorney but I did spend 27 years as a "boss" in a non-govt. job and have on at least one occasion stayed in a Holiday Inn.
If they gave your brother the choice of resigning or staying and attending anger management courses, it would appear to me they would have a tough time proving gross negligence. The question would be if he was guilty of gross negligence, why didn't they fire him immediately?
I don't see how the employer could deny him COBRA if he resigns. If he does, he needs to do so in writing and give two weeks notice to be on the safe side. Since they've already said they would give him two weeks pay, I'm assuming they will do that in lieu of him working the two week notice period.
Is he aware COBRA requires he pay both his and the employer's premium, which could add up to a substantial chunk of change each month?