Wow,this really is confusing.
Welcome to the American judicial system. This is one of the reasons attorneys in the US can only practice in one state.
In Sweden there is only the law clerk, who helps the judge with writing decisions, researches pre-trial stuff, sits in on trials and calls out cases and parties, takes notes, records the statements on a CD. They can also take smaller cases like petty theft on their own. You have to have a law degree to be called a law clerk and in order to become a judge you have to be a law clerk for two years and get very good grades for doing that job. Otherwise you wont be able to make it to the next level.
In the US, such a law clerk would probably be fresh out of law school, and work in the position for one year before going on to another job. In Superior Court one law clerk would probably work for quite a few judges, and would mainly assist the judge in researching law and helping write decisions. They probably would not call the case. They would only sit in on a trial when the trial is really interesting. They would never take a case on their own.
The following thread might help you with understanding how to become a judge in California: http://ca.lwv.org/lwvc.files/judic/. What the article doesn't mention is that judges are going to have some level of involvement with either the Republican or Democratic party and will probably know the governor.
My scene is pretty small and deals with a domestic violence case and a custody case.
I'd put it in the family branch of the county Superior Court. It could also possibly be heard in the municipal court. And to further complicate matters, I believe Britney Spears' family woes are being heard in the Federal District Court, although I do not understand how it has jurisdiction.
I'm just wondering if the two judges from those cases realistically could meet in the same building and if the law clerk would be able to know both judges.
Definitely possible for judges to know other judges in superior court, as that's a big building. I don't know how many superior court judges LA county has, but it's going to be at least 10. This is one of the busiest courts in the country. You might want to look at http://www.lasuperiorcourt.org/aboutcourt/.
The law clerk could be assigned to both judges, as there usually is not enough work for one judge at the superior court level to justify a law clerk to be dedicated to the judge. Most cases don't involve much new and different law.
I'm also after a court position that would signify a pretty newly graduated law student's want to become a judge, similar to the law clerk position in Sweden.