Katie has stated herself that if Hermia had stayed with her father it could have been dangerous. If you are threatened with death, then you need to get yourself away from that situation.
If your parents threatened to kill you, of course you would run away! I believe that someone would do that, even if a lover was not involved, and because a lover was involved, this just intensified the reason for running away.
No parent should control their child’s life in this way. Hermia is old enough to make her own decisions; she does not need her dad controlling her every move. Even if it was a mistake to marry Lysander, it was Hermia’s mistake to make.
She did the right thing by following her heart and removing herself from a dangerous situation.