Had the dog bitten a person, the owner would be strictly liable even on their own property if there was an implied invitation to come over because California is one of the few states with that specific law.
Since the dog bit another dog, you'll want to check local city codes to see if your city has over like Beverly Hills does which makes a dog owner liable for any damage done by the dog. Do NOT expect the JP or judge to know about that law. YOU should check and bring it to the attention of the court if there is one.
Assuming no city code creates strict liabilty, under state law you can prevail by showing that the owner (registered owner aka dad or de facto owner son) KNEW that the dog was aggressive. Choosing to keep an aggressive dog makes the owner liable under California law. That's called scienter.
If you can't show that they knew the dog was aggressive, the fallback position is their failure to effectively control the dog. Dog owners have a legal duty to control the animal
The question my arise whether you took on the risk by going over to the dog. Binding precedent says no. You may want to jot down these citations:
Playing with a dog and patting his head did not constitute assumption of the risk. Smythe v. Schacht (1949) 93 Cal.App.2d
In Burden v. Globerson (1967) 252 Cal.App.2d 468 the court ruled that regardless of the dog's breed, one does not assume the risk of being bitten simply by choosing to initiate interaction with a dog.
See also:
http://dogbitelaw.com/statutory-stri...alifornia.html