"His attorney did an admirable job yesterday in court."
However, when we speak about going to a particular court on legal business we are more likely to use "at."
"I will meet you tomorrow at the county court." This implies that you are meeting at the courthouse building.
Now, if you are interning, I would assume you are planning to work at court, doing a variety of tasks that may not be happening only in a courtroom.
I am not very schooled in legal internships, however, so someone else may have a better idea about this.
Student or Learner