@DanPhelps88 Welcome to the community!
This is exactly right! However, へ (or に) is used in tandem with the whole phrase あそびにいく to indicate the act of “going to to go play” rather than just “to play” (あそぶ).
〜にいく pairs with other verbs to give them direction/motion and expresses what you are moving toward (to do). Therefore, it is better to think of Verb + にいく as one phrase, rather than trying to connect particles to only the first part of the phrase.
I hope this helps. Cheers!