There are stop signs all over my local Wal-Mart parking lot and they mean nothing other than Wal-Mart can ask me to keep out if they don't like me running them.
But the law in PA is that you must have a learner's permit to drive a car anywhere. (I guess your own private property might not apply.) So they were breaking the law by letting her drive.
You know just enough about the law to be dangerous.
If the dad didn't own the parking lot himself or he didn't have ongoing business with the owner, he shouldn't have been there for any reason at all. A case could be made for criminal trespass.
True, parking lots are not normally policeable areas if the owner doesn't want the police. There are exceptions for health and safety, and for felony violations. I can assure you that if WalMart wants the cops to write you a ticket for speeding in their parking lot, and the officer observed you violating the law, you can be ticketed and punished accordingly. My WalMart has cops sitting in the parking lot on Friday and Saturday night to keep the high school kids from racing through the lot, endangering paying customers. Many, many tickets were written every weekend, until the punks got the message.
In most jurisdictions, law enforcement cannot enter private property without a warrant unless called in or he/she observes a felony offense being committed. I don't know how many hundreds of DUI cases I have seen sucessfully prosecuted where the offender walked out of the barroom (visibly drunk) and get into a vehicle, only to be apprehended, cuffed, and stuffed before he/she left the bar's parking lot. You don't really think the club owners wanted to have their patrons hassled right outside the front door and gave permission for this, do you? The cops had the right because they personally observed a felony being committed, and they arrested the offender before that person drove away killed someone.
Quit watching Law and Order or NYPD Blue and go to the law library, or pull a copy of you state and/or local statutes. I think you might be amazed.