You don't have to wait for me. I have to get my wallet in the car.
I forgot my wallet in the car. Why don't you go home ahead of me?
ーYou don't have to wait for me. I have to get my wallet in the car.
「私のこと待たなくていいよ。車にお財布取りに行かなきゃいけないから。」
don't have to wait for someone で「人のことを待たなくても良い」＝「先に帰ってくれて良い」というニュアンスで使います。
get には何かを取ってくるという意味もあります。
ーI forgot my wallet in the car. Why don't you go home ahead of me?
「車に財布を忘れてきた。先に帰ってて。」
forget ... in the car で「車に…を置き忘れる」
go home ahead of me で「私より先に家に帰る」
ご参考まで！
カナダ 
