Hello!
I hope that you have been able to address this problem already, by if not, perhaps I can help.
First, I applaud your use of assertions (or other checks) to insure correct behavior of your code, and the avoidance of problems with user input. As you're aware, these are common practice in software engineering. Any solution to your problem should not immediately involve the removal of such checks, as long as the checks, themselves, are correct.
You mention "[the] problem is that the customer has two children with their own daughter...". I'm not able to determine for certain what this statement means in the context of genealogy, but I assume that some family tree built by your customer has resulted in one or more checks (assertions) to flag a problem. This being the case, my first thought is to ask whether the check(s) are, in fact, flagging an issue that you believe is, truly, incorrect? If this is the case, then your customer is not using the software correctly. On the other hand, if the situation flagged is something that you haven't considered to be possible (or likely), perhaps your customer has presented a legitimate situation which you should consider addressing, to allow the tree as presented to be valid. If this is the case, then modifying the existing checks, which are involved in reporting this situation, should be adjusted to recognize that it is legitimate, which still checking of other erroneous conditions.
Let's assume, for the moment, that the statement "[t]he problem is that the customer has two children with their own daughter" means that the customer has two children, and these two children are [considered to be] the parents, jointly, of a daughter. (This might happen if the two children jointly adopt a child, or if the 2 children are [step] brother and sister, and have had a child.) Let's also assume that your software is explicitly disallowing 2 siblings from being parents of the same child. Clearly, it is physically possible, if not generally acceptable by society, for two siblings to be parents of a child; therefore, your software would be more restrictive than necessary by disallowing this possibility. Also, clearly, it should be possible for you to remove (or modify) this (particular) restriction, without affecting other such restrictions.