losing a parent during internship

I found out a few hours ago that my father died unexpectedly in an accident, and I'm not really sure how to handle work tomorrow. I was estranged from him and didn't grow up with him. He lived in my family's native country while I was raised in the U.S., so we never had much of a relationship.

I think I would be capable of working tomorrow, but I'd really prefer to work remotely so I can process everything privately and not have to be around people in the office. The problem is that I already worked remotely twice this past week because I had been feeling down, so I'm worried that asking again will make my manager think I'm unreliable or incapable of working.

Do I need to tell my manager specifically that my father died? Or is it okay to just say there was a death in my family/personal situation and ask to work remotely?

I'm mainly looking for advice on whether this is a reasonable request and how much information I actually need to disclose. I don't want to overshare, but I also don't want my manager to think I'm just repeatedly asking to work from home because I don't want to come into the office. I haven't gotten any bad feedback from either of my managers, but they're kind of hard to read and mostly just talk to each other out of assigning me work to do. 😭