I got on a train going the opposite way and didn't realize until two stations later.
The reason I was late is because I got on a train going the opposite way and didn't realize until two stations later.
ご質問ありがとうございます。
この場合は、「反対方向の電車に乗ってることに、２駅進んでから気づいた」は英語で「I got on a train going the opposite way and didn't realize until two stations later.」と言えます。
遅刻した理由をあげたいなら、最初「The reason I was late is because...」から始まれます。
最終的に「The reason I was late is because I got on a train going the opposite way and didn't realize until two stations later.」になります。
ご参考になれば幸いです。
I got on the train and went in the opposite direction. It took me two stops to realize it.
この場合、次のような言い方ができますよ。
ーI got on the train and went in the opposite direction. It took me two stops to realize it.
「電車に乗って反対方向へ行ってしまったが、２駅過ぎるまで気が付かなかった」
to go in the opposite direction「反対方向に行く」
to take someone two stops to realize it で「気がつくのに二駅かかる」
ご参考まで！
アメリカ合衆国 
カナダ 
