Well, you have to make up your own mind whether to stick it out or quit and go elsewhere. Business
might pick up; then again, it might not.
If you do decide to quit, the professional thing to do is to give two weeks' written notice. Thank him for the opportunity, say it was a positive experience and a pleasure, but the time has come to move on.
Having worked for a small family-owned company, I will tell you that an owner will always favor his/her own family members over non-family employees. So it doesn't surprise me that the owner gave the shifts to his daughter.
Is it legal for him to give away beer if he doesn't have a liquor license? Even though he's not charging for it?
Good luck with whatever you decide.