いーってなる is a colloquial/slangy expression to express a state "enable to endure being irritated".
By the way, that sentence is ambiguous. Grammatically, two interpretations are possible. The one who is not irritated can be both 姉さん and 補佐.
姉さん is the subject of いーってならない (i.e., 補佐 is the subject of 一緒にいる)
姉さんが、一緒にいてもいーってならない人 (=一緒にいても、姉さんがいーってならない人)
補佐 is the subject of いーってならない (i.e., 姉さん is the subject of 一緒にいる)
姉さんが一緒にいても、いーってならない人
Only the context can tell which is correct.