If the man really did have his hands down the daughter's pants, and the father beat him up some but didn't do any permanent damage, you let it go. If the man stopped to surrender and the father beat him so badly he broke both of his legs and ruptured his spleen, the father continuing to beat him after he was unconscious, then the father gets charged. There is definitely a grey area in there that can be hard to decide on.
Okay then, as it relates to the OP, the woman hit the man only hard enough to make him collapse and drop the purse.
And as it relates to immediate threat, the man ran away and there was no longer an immediate threat to his daughter. He had no "legal" reason to chase the attacker.
Hitting someone with a stick and running someone over with your car are different things. While nothing is certain, it seems much more reasonable to think a person can more easily limit the damage done with the stick than with the car.
I don't know that the man in your hypothetical would need a legal reason simply to chase the attacker, but a citizen's arrest is one possibility. It is having no legal reason to assault the attacker after catching him that is the crux of the situation. In the end, such an action, as you described it, would be illegal. If a prosecutor decided to pursue charges, the man might well be convicted. My response is based on my own feelings considering the circumstances, not the letter of the law. I think that at times, mitigating circumstances should be taken into account. That may well happen with the woman who hit the thief with her car. What she did was likely illegal, but that doesn't always mean a person ends up prosecuted. The charge could be dropped, or if it goes to trial, a jury might decide not to convict.