Scheduled to work outside at night with 〜ことになる

Grammar Explanation: To end up being with 〜ことになる

Kate says she wants to study together with Emiriko before bedtime.

エミリコ:: 「あっ…　ごめんなさい。実(じつ)は外(そと)の仕事(しごと)を深夜(しんや)にもすることになって…」; “Ah, I'm sorry. The truth is, I'm scheduled to do late-night work outside...”; Literal: “Ah... I'm sorry. Actually, it has become the thing that I also do outside work late at night...”; 「また別(べつ)の機会(きかい)にお願(ねが)いします！」; “Please ask again another time!”

Key Points

1することになって points to an assigned plan

外(そと)の仕事(しごと)を深夜(しんや)にもすることになって means Emiriko has been scheduled to work outside late at night too.
The sentence trails off because this explains why she cannot study now.

2実は introduces the real reason

3また別の機会に politely postpones

実は (Actually): 実(じつ)は introduces the truth, often something the listener did not know: “to tell the truth”.
外 (Outside): 外(そと) is the outside of something, or outdoors.
仕事 (Work): 仕事(しごと) is work done for a living, or a particular task one has to do.
深夜 (Late night): 深夜(しんや) means late at night, usually after midnight.
する (To do): する is to do or perform something. It also turns many nouns into verbs, as in 勉強する.
こと (Thing): こと is an abstract thing, matter, or fact, as opposed to a physical object. It also turns a verb phrase into a noun, as in 見たことがある. It is also written 事(こと).
なる (To become): なる is to change into a different state or become something. It also means something turns out a certain way. It is also written 成(な)る.
また (Again): また means “again” or “once more”. It also means “also”. As a goodbye, またね means “see you”.
別 (Separate): 別(べつ) means another or different one: “separate” or “other”.
機会 (Opportunity): 機会(きかい) is a good time or chance to do something.