"우리 아버지께서 쇼핑하러 가세요."
Translation:My dad goes to shop.
The expressions (으)러 가다/오다 are used to express why the subject came or went somewhere. So it would only be, "My dad goes to shop."
The expression attaches to the verb stem/infinitive form of the verb 쇼핑하다 (remove 다 and add the expression), which means "to shop."so it is like using the infinitive of the verb as an object.
The grammar is actually (으)러 가다/러 오다. For example 하다 becomes 하러 가다, or 먹다 would become 먹으러 가다.
It expresses what the subject came or went to do. If you went Korea to study Korean, and someone asked you why you came to Korea, you could respond 저는 한국어를 공부하러 왔어요. "I came to study Korean."
Toby, yes usually this would be correct however not in this case. The “to” in this sentence is not a preposition (expressing direction). It’s being used to express the reason the father is going. i.e.“She goes to eat.”. Because there is little context this is difficult to establish and most people would understand this sentence just as you have.