Here's what I do:

1. Move all characters close to the quest-giver. Within the "interaction radius" (where the mouse cursor would turn to gold instead of grey).

2. Right-click quest giver on main character.

3. Press a keyboard button. This makes all other chars /assist and /interact with the same quest giver. This button works exactly the same as casting a regular spell. It uses a "/assist [shift][alt][ctrl] Name" combination macro to assist whoever my main character currently is, then trigger an action on my action bar. The action is a macro that just says "/interact". There's a slight difference from normal spell-casting, in that this keyboard button only executes on my other characters, not the main character.

4. Hold ALT and mouse-click "Accept". This broadcasts a mouse-click on that screen position for all characters. Note that all my characters use the exact same UI layout and screen resolution, so all UI matches up everywhere.