The likely background
The boss probably knows, what is he doing. Probably he knows very well that employing his daughter is more harmful for his company as employing someone else with a more neutral background. The likely reason for him to do this, that he is willing to pay this price, in the sake of educate his daughter.
You can't be sure, what price is he willing to pay for that. It is quite possible that he is willing to fire you in the case of an open conflict with his daughter.
You have to test the boss, what is he willing to pay. Make a test maneuver, how the boss will react if the conflict with his daughter would escalate. How can you test him, it depends on your circumstances.
For example, you can mention his daughter in a neutral context, or in a nearly neutral context. Or, you can watch, how the Boss reacts if your daughter has a conflict with others. Watch closely his face. Try to understand, what is he doing and why.
From the result, you have to estimate, until when can you go.
Until you don't have a clear image, what is the work relation between the Boss and the Daughter, handle the Daughter carefully. I would suggest to accept what she wants. Consider she as a "Crown Princess". Try to get her trust, or at least a neutral stand.
If the Daughter has also conflicts with others, then be silent, watch closely, and go back to (1). If she has conflicts only with you, you should choice, until which point can you go in a conflict.
It could be also useful to give time to the Daughter, maybe she doesn't really know, what is she doing. The Boss is likely closely watching her, and continuously instructs her, what to do, how to behave.
Even if you decide, the situation is intolerable, step out professionally. Yes, I know, it means you will have to "swallow a lot of poison", and it will be hard. But the Boss will know this, and this is exactly what also he will consider as you step out.
Try to avoid open conflicts with the Daughter, and if you decide to leave, do it in good standing. If you feel, what she is doing is extreme, swallow it. Later, in the far future, it will be judged as a big positive thing from your side.
Also this is possible, that the Boss will teach his Daughter, how to behave with the employees. On the sudden changes of her behavior, you will see what instructions had she got from him.
In this case, accept that from the Daughter and be forgiving. Helping the first "wing beats" of a member of a family company could result for you lifelong respect in the company, and thus, stable job.