Does the actions of one's ancestors pass down?
People, beings find together of cause their inclinations. Relations usually as well. And grandchilden are often rebirth of their anchestors as well. Don't one forgeth that as well. So it would be not correct to say that there is no connection as there is a long time feed each other behind. So take care with whom you chose to associate. At least the smell will be on you.

That goes also toward your own behavior. Others, with similar origin may suffer from your possible behavior or benefit from your reputation according to their individual kamma in addition. There are no such as innocent phenomenas, people, as well as there are no "guilty" ones. Causes have effects and they lead all back to ones past and present deeds on touch.

But the fact that people, beings, are after the same food, certain conditions, does not mean that they act always equal. What ever one does identify oneself with it, is sooner or later suffering. So that's the reason why best possible relations are seeked to go beyond relations. It's not possible to say that you are lucky or in big misfortune to ever asked here, whether you get touched physical, or mental, right or wrong for your best, who could decide for you where to put attention on? Who could prepare your required foundation to receive what gives liberation?

See also Why beings take birth, even in most worse existences and circumstances?

So it's good to think on: Darkness here as well. "May all beings make the right choices to gain happiness for themselves with ease", is a good thought to leave it.

(Note that this is not given to leave one in trade, exchange, stacks bond, but as a tiny door for an exit.)