"They have forced the children to finish their food."
Translation:De har tvingat barnen att äta upp sin mat.
"Sin" refers to the subject. So, the children are not eating their food (in their plate), but instead eating the food of "they/adults"... Did duolingo wanted to say that?
No, "sin" refers back to "barnen" here, not to "they". However, it's a good observation of yours. This is the way it works in a sentence like this. Had it being referring back to "they", it would have said "deras". I'm sorry if it's a bit confusing...
That is in fact confusing. I was thinking so far that SIN was always his/her whereas DERAS was their
"Sluta" cannot take "mat" as an object, it just sounds weird. In Swedish, food is not something you can finish, but something you eat up. You can "sluta jobbet" (quit work, get off) though. And it's perfectly fine to sluta + (att) + verb.