YOU SAID:

Im going to the store, take care of the house while im gone

INTO JAPANESE

私は店に行き、行っている間に家の世話をします

BACK INTO ENGLISH

I go to the store and take care of the house while going

INTO JAPANESE

店に行って家の世話をしながら

BACK INTO ENGLISH

While going to the store and taking care of the house

INTO JAPANESE

店に行って家の世話をしながら

BACK INTO ENGLISH

While going to the store and taking care of the house