She didn't join in our conversation.

Literal

She [topic-は] our conversation [to-に] join-not-did.

加わる ('to join, to participate, to be added') is intransitive — it's about becoming part of something rather than actively grabbing it (which would be 加える, transitive). The に here marks the target of joining: '~に加わる' = 'join ~.' 会話 ('conversation') refers specifically to verbal exchanges; for joining a group or activity broadly, 加わる pairs with target nouns like グループ, チーム, or 議論 ('discussion'). The negation 加わらなかった quietly notes her non-participation — perhaps from disinterest, shyness, or disagreement.