Please take off your fur coat and make yourself comfortable.

Literal

Fur-coat [object-を] take-off-[and-て] please relax-[do-て-please-ください].

楽にする ('to make [someone/oneself] comfortable') is the causative-type collocation using 楽 ('easy, comfortable') + する. ~てください after the suru-phrase gives the polite request. The sentence chains two verbs with a te-form: 脱いで + 楽にしてください ('take off and make yourself comfortable'). A classic hostess welcome line.