Is she sinful if someone asks her, while she is angry, to drink juice, and she refuses despite his swearing by Allah? And what must she do for Allah to forgive her?

Fulfilling an oath is commendable, not obligatory. So, if you do not respond to him, there is no sin upon you. It is commendable to respond to him so that you may be rewarded for it. If you do not respond to him and his oath was binding, then an expiation for breaking an oath becomes incumbent upon him.