"We will go to the beach to swim."
Translation:수영하러 해변에 갈 예정입니다.
There is a focus-shift in the two sentences.
(1). The given example:
수영을하러 해변에 갈 예정입니다 - I will go to the beach (in order) to swim/to have a swim.
Focus on purpose of going.
(2). Your answer:
해변에(서) 수영을하러 갈 예정입니다 -
I will go swimming at the beach.
Focus on the activity itself "swimming" ( "go" in this case acts as a form of auxiliary verb meaning more or less, to participate in.)
- When 러 is placed immediately before 가다 :
Verb+러 가다 = go V-ing
수영하러 가다 = go swimming
It is because the main verb, ie. "to go" starts somewhere else (e.g. home) and the activity ends at the location of the beach. The beach is therefore only a destination, and not the location of the action.
The beach is also the implicit location for the verb "to swim", but if it applied to this subordinate clause, the English sentence would read: "We'll go to swim at the beach." and that would be "해변에서 수영하러 갈 예정입니다"