Don't talk about work when we're on a trip.

Literal

Travel-destination [at-で] work [possessive-の] talk don't-do [request-よ].

~しないでよ is a casual negative request — 'don't do X, please.' よ adds mild emphasis/pleading. 仕事の話 (work talk) uses の to connect the topic to the noun. A very natural, colloquial complaint about mixing work and vacation.