YOU SAID:
We went late to the party
INTO JAPANESE
私たちはパーティーに遅れて行きました
BACK INTO ENGLISH
We went late to the party.
INTO JAPANESE
私たちはパーティーに遅れて行った。
BACK INTO ENGLISH
We went to the party late.
INTO JAPANESE
私たちは遅れてパーティーに行きました。
BACK INTO ENGLISH
We went to the party late.
That didn't even make that much sense in English.