I think it is about her baby meeting his cousin for the first time. You need to break it into pieces. ベビちゃ baby 初めて first time 従兄弟の cousin's お兄ちゃんに brother 会えました met However, I think cousin's brother is just identifying the type of “brother” (note the の). Your male cousin is one type of "brother" in Asian families. I had a young Chinese friend tell me her little brother was coming to visit, but it was really the son of a friend of her mother.