that just pmo why the hell would she drink it

To show the emperor that someone was trying to poison/kill him. If she had just thrown it on the ground, there would be no evidence. It's a lose-win situation.

Cuz the Duke might reuse his powers on her again. Although the brainwashing is break he might redo it (he was just close by). She need to take fast action so the emperor would be wary.