You're fast, trick him!

You've got to think fast, or the woman dies. You decide to just go for it. You run at him, and before his axe can even touch the woman you've already connected with your first punch, right to the face. He stumbles back which the mother uses to escape his grip and run to safety. This obviously enrages the bandit and he charges at you with rage in his eyes. That rage also makes him sloppy, and so you use his lowered defenses to deliver another punch, this time right to the gut. His axe falls to the ground and he to his knees. Defeated and barely able to breathe he says "The captain will make you pay for that!" as he stumbles away to the woods.

You run to the mother and the girl to look after them. You're glad to see neither of them hurt, but quickly take off to run after the bandit, before you go the mother grabs your arm and says "If you really manage to defeat these bandits, come find me for a special reward." Motivated by this and the Prospect of kicking some more ass, you run into the woods...