Como é que se diz isto em Inglês (EUA)? 帰国されたら、ゆっくりなさってくださいね。(At the airport, to your client going back home.)

See a translation

For this phrase, I would translate it in one of the following ways:

“I hope you are able to take it easy once you get back home.”

-“take it easy” is a little bit of a casual phrase. However, friendliness is valued in English communication, even in many business contexts, so I think it would be ok to use.

“Please take a rest after you arrive home.”

-This phrase is also alright, but it does seem a little stiff possibly. But if you say it with a smile and a positive attitude, it shouldn’t come off as unfriendly in a business environment.

“Please [do something]” is also a little bit direct, so you could also soften up the phrase a little by changing it to “I hope..”

→”I hope you are able to get some rest after you arrive home.”