How to handle court appearances 4+ hours away?

Hello, just looking for advice! I started a new job at a large firm 1.5 months ago. Up until now I have been performing writing tasks for the firm, but no cases of my own. I come from a different practice area as a background and have been an attorney for 3 years.

My problem at present is my job is remote (not everyone but I was hired as remote). They are now looking for me to cover cases 4 hours away (I live in a large state). I would have to take public transport and these cases are all morning docket. Client does not allow time to be billed for travel or waiting for conference to be called. Does not reimburse travel or hotel cost.

I dont want to be seen as someone who always dodges appareances. How do I navigate not wanting to wake up at 3am to leave my house at 4am to travel for 8 hours of non-billable time and a $120 in train tickets? Ita not fair to make the other person in my practice group always cover but also this will be a huge monetary and time cost and seriously hinder my ability to meet billables.