The "am" is used to infer that she wants to have a word with her. It's rather idiomatic.
Is there also a similar construction for a negative clause without "dim" meaning "Sioned does not want to have a word with you."? I could imagine "Mae Sioned yn erbyn air gyda ti."
That would be similar to German "Sioned ist dafür/dagegen, ein Wort [hier besser: ein Gespräch] mit dir zu haben." Or in English: "Sioned is for/against having a word with you."