"Mereka pulang ke rumahnya, yaitu ke Jakarta."
Translation:They return to their home, that is, to Jakarta.
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Yaitu means that is only in the sense of i.e., that is to say, in other words, to put it another way.
English is tricking us as it lacks a simple word for “that is to say.” If this were, let us say, a Finnish to Indonesian course, we wouldn’t have that problem (but we’d have some other problems instead).
Also, you are overlooking comma number two in the English translation—otherwise it wouldn’t fit “that is in Jakarta.”
You could put it like this: In the example sentence, they return to their home Jakarta, in your alternative translation they return to their home in Jakarta.