、。
Mother was at a complete loss over what to do with all that mess.
Literal
Mother [topic-は], that scattered things [obj-を] what if-did good [question-か] troubled-ended-up.
どうしたらいいか is an embedded question meaning 'what (one) should do' — literally 'if one did how, would it be good.' The か turns it into an indirect question that serves as the object of 困る. ~てしまう adds a note of regret or completion — 'ended up troubled,' 'couldn't help being at a loss.' 散らかる is intransitive 'become scattered/messy'; its past-adjectival form 散らかった modifies もの.