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So I have a judicial internship lined up for the first 6 weeks of the summer. I am hoping to get an internship in a firm for the last 6 weeks. I have accepted an interview from a firm but the application did not require a cover letter so I was unable to communicate my specific circumstances, i.e. that I am not looking for a full summer internship.

Should I bring this up in my interview, or should I contact the firm directly now?

I found out and applied to the firm through Symplicity, a school website to connect students with employers. If I were to contact them directly however, I would not be able to do it through this website. I would have to go to the firm website.

What’s the correct course of action? Thanks!

Just talk about it at the interview -- they'll tell you about how they run their internship program, and if not you can ask questions.

If it's a paid internship and they want you to whole summer, I would seriously consider withdrawing from the judicial internship. Your career advising office will hate that and tell you not to, but an internship is not a clerkship and it's just not a big deal.

Secure the offer, don't mention the internship, ask to split later. Agree with the above as long as it's a medium/big reputable firm and not some shop where you're making $15/hr.