What you’re saying is that children should carry the responsibility for the acts of their ancestors.

No. I'm not saying that at all. I'm saying that people carry the responsibility to choose against unfairness if they have a choice. Whether the unfairness was created by your ancestors or someone else's is irrelevant. If you are in an unfair position thanks to past unfair acts, and you can choose to let go of that position (or do some other action) to remove that unfairness from the world, then you should. Or, put otherwise, you don't "deserve" that position, because it was attained unfairly.

Who’s the judge calculate the outstanding balance they both will naturally come to the conclusion that they’ve been unjustly treated

Well, I'm just stating that forgetting the past is not a good ethical standpoint. It is reasonable to believe it's at least a practical one, and maybe it's interesting to reason about the role it should have in lawmaking, resolving conflicts on a case-by-case basis, etc., but that is far from applicable in this case, or in general. I find no reason to use that simplification (which gives different outcomes) unless we're in a situation where it's become really difficult to reach consensus.

What if it turns out that your grand grandfather was a soldier who brought home some gold of dubious origins?

Then I would have the obligation to act according to it (return it, etc.). I would still have the right to get that wealth back, but then I would be forced to do something with it.

Anyway, I think I might be overexplaining and making it way more complicated than necessary. Everything I said can be summarized as follows: people have the right to not be affected by anything outside their control. Managing to provide that right is equivalent to effectively deleting the effects of every past and present unfair action. For example, if you properly redistribute wealth, then all of this family wealth robbery stuff simply fades away over time, as redistribution favors differences of recent origin and smooths out older variations.