Well there are a few factors which make this situation different. If the ultimatum had been made in person, I'd think there might be room for negotiation, depending on the relationship between manager and subordinate.

Putting the ultimatum in e-mail form really raises the stakes, because there may be other people CC-ed or BCC-ed, and any response could later be weaponized.

If the relationship was already troubled, anything like an ultimatum is an opportunity for the manager to be rid of all their troubles.

The level of the threat also comes into play, and more severe threats increase the risk/tension. If the guardian had threatened to disown the child rather than send them to bed, we would read the situation differently.