If your parents are calling you to do things, your best bet is to ask if there's anything they need before you queue. Maybe even be completely up-front: "Hey, I wanna go play a game that requires me to be active for about 30-50 minutes, so I wanted to be sure you don't need anything before I start it."
Alternatively, sit down and have a genuine conversation with them about the game - how it works, what it demands of you, that sort of thing. Explain how it's a matter of responsibility: by queuing for and joining the match, you've agreed to play the game through, and help your teammates for the entire duration of the match. Stress that bailing in the middle of it is rude and disruptive to those other players, in addition to being a generally irresponsible act on your part. Try to find a compromise between their needs on your time, and your desire to play.
Hopefully, a conversation like that will have two major effects: it will allow you and your parents to come to an agreement about when you can play (setting aside "safe times" for you to queue, or a system of communicating that intent to create such times), and/or it will allow them to better understand why you can't simply drop the game when they call, so they may be more forgiving when you answer with "We're 10 minutes into the match, I'll do it as soon as we're done."
I may be able to offer more specific advice if you don't mind saying what kinds of things they usually call you away for.