@McTag,
Quote: There's a suggestion of future in the question so "do" is not a good fit.
In English DO/DOES/PRESENT SIMPLE is often used for the future.
A: Do you leave tomorrow? B: Yes, I leave on the 10 am flight.
You want to go to the movies tonight, don't you?
She goes to university next week, doesn't she?
In the OP's example,
I trust you won’t mind if we leave early, ... you?
it gives the feeling like the speaker shifts mid sentence, adds a slight pause and uses the more direct DO.
Quote:"Would" would work too, but is not given as an option.
But it is a fine addition, a more polite, more deferential choice.