、。
Tomorrow I'm taking my mother out in my new car.
Literal
Tomorrow, I [topic-は] new car [with-で] mother [object-を] take go-out [polite-ます].
で here marks the means or instrument — 'by car.' つれて is the te-form of 連れる ('to bring/lead someone along'), and the compound 連れて出かける chains 'taking [person] with' + 'go out' = 'take out.' Japanese handles 'take [person] out' through this compositional strategy.