Yes I agree!!
I also assume that he left her with a daguer to defend herself, not to kill herself (He told her to "Hold on") and sent the Crown Prince (his student, that from how we can see from the story so far has no reason to care about the poisoned princess, his sister) to help her escape. Which would make sense with his "Hold on" (---> hold on until the prince comes to save you)

what happened in the past was a MISUNDERSTANDING! a big misunderstanding, im sure the father left her to find the real culprit and prove her innocence....