I reached a certain part in my story, and I realized that I wasn't sure if the passengers in Second Class wore different clothes for dinner than they did during the day. Did they?
Yes. Second-class passengers were most likely a part of the middle class (middle-middle and upper-middle), and though they might not have dressed as fine as multi-millionaires and their wives, they followed the popular edicts of the day which required clothing for each occasion of the day.
In fact, a number of the second-class passengers would have been traveling in first-class on other ships, and weren't at all happy about the downgrade.