He feels more at ease when his brother is with him so he gets a bit over-excited.
He feels more confident when his brother is with him so he gets a bit over-excited.
この文脈で使う「安心」は英語で「feel at ease」になると思います。しかし、「feels confident」(自身が出る)という言い方も使えると思います。
「兄が一緒だと安心するみたい」
He feels at ease when his brother is with him
He feels confident when his brother is with him
「うるさいくらいなんだけど。」
so he gets a bit over-excited
「over-excited」という表現は「興奮する」という意味になりますが、この文脈に使ってもいいと思います。
「兄が一緒だと安心するみたいで、うるさいくらいなんだけど。」
He feels more at ease when his brother is with him so he gets a bit over-excited.
He feels more confident when his brother is with him so he gets a bit over-excited.