Is there a different word for "that" in Swedish? So far I've only seen "det/den", but when I put in "that", it is often marked wrong. I understood the sentence would be in the context of a schedule, i.e. "I'm responsible for my coworker's kids. That's my day today." Is that actually wrong? Or should "that" be acceptable as well here?
"that is my day" would not be used with "today" (this day) in English. "that" implies something over there, not very close, not part of me.
"It is my day today", is almost like the day is part of me. Tomorrow is Saturday, that is (or - it is) my birthday. There are lots of exceptions and variations, but it is a useful guide to think of "that" as indicating not near in place or time.
That's not necessarily true. I'm a native English speaker, an English teacher, and a writer/editor for a magazine, so it's literally my job to think about grammar all day. : ) It depends on the context. For example, if you think of "It's my day today" as meaning either "Today is the day everything will go right for me" or "Today it is my turn to do something," then yes, you'd have to use "it." But consider the following: "I have work in about half an hour. There's a big meeting with the shareholders at 11:00 followed by lunch with my coworkers. After work, I need to go to the supermarket. Dinner is at 16:00. In the evening, we have plans to watch a movie. That is my day today." In this context, "it" wouldn't make any sense. You need "that" because it's referring to the schedule described in the previous few sentences. So with the example I gave in my last comment, you could use "it," but it would change the meaning. "I'm responsible for my coworker's kids. It's my day today" would mean "today it is my turn." But "I'm responsible for my coworkers kids. That's my day today" would mean "that responsibility takes up my entire day. I have no other plans, or no time for other plans." It depends on the context, and there are plenty of situations where "That is my day today" is a valid sentence. So unless there's some reason you can't say that in Swedish (in which case I would like to hear the explanation so I can better understand), I think "that" should be an acceptable answer here.
Surely "That is [what] my day [will be] today" is the full length version?
Contractions with "is", "are", "has" and the like are usually created automatically by duolingo. Vexingly, this usually only applies to pronouns though. Anyhow, I added it manually now.