Context:
今日は午後からまつ毛パーマをあてに行きました。
What is the difference between "まつ毛パーマをしに行きました" and "まつ毛パーマをあてに行きました"?
The verb あてる is used for "get" in "get a perm". (まつ毛)パーマをあてに行く means "go to get a perm". We also use the verb かける for this. I don't see much difference between (まつ毛)パーマをあてる and (まつ毛)パーマをかける. I personally don't say (まつ毛)パーマをする/パーマをしに行く but it seems that some people use the verb する and it sounds okay to me.