"저는 할머니의 댁에 가요."
Translation:I go to my grandmother's house.
댁 is an honorific word for 집 like 진지 is for 밥. Honorific words are used in the context of respect for the person being spoken about. 댁 is an esteemed person's house and 진지 is something an esteemed person eats.
"I am going" should also be accepted - I know that technically you can say 가고 있어요 if you really mean, like, right at this moment, but 가요 can also be translated as "am going"
I would guess that is because "grandma" does not show respect for one's grandmother.
Everyone knows the song... It might not be the most proper thing in the world to start sentences with prepositions, but it certainly isn't improper to say something like this. Unless you don't really have a sense humor...