娘が無事に着いたかどうかと思って電話をかけようとしたが、通じなかった。

、。

I tried calling to see if my daughter had arrived safely, but I couldn't get through.

Literal

Daughter [subject-が] safely arrived [whether-かどうか] [quotative-と] thought phone [object-を] try-to-call [but-が], did-not-connect.

かどうか = 'whether or not X.' Embeds a yes/no question as a noun. かけようとする = 'try to call' — volitional + とする marks attempted action. 通じる ('to be connected, to get through') is the verb for phone connections (or understanding). A parent's anxious moment.