[dpark]

HR isn’t there to help you out. They’re there to protect the company. This scenario is not one that HR is likely to get involved in and it’s more likely to put you on HR’s radar as a “troublemaker” than anything.

If you want to discuss it with the manager’s manager, CC on an email is the wrong way. Talk to them privately. They may or may not be sympathetic but this is more likely to work than an obvious attempt to shame your manager in front of their boss.