Cancelled flight & rescheduled 3days later, compensation??

My family of five went to NYC for a couple of days this week, we are originally from Toronto. On our way to the airport to catch our return flight (Saturday) to Toronto we got an email that our flight had been cancelled. We were automatically rescheduled for a flight on Tuesday. Which is not reasonable, we work and have school. Not to mention that’s very expensive to stay. Because we were already in the airport we went to the Porter desk to ask why a 3day wait and what was up. Their original email never said why the flight had been cancelled even though my Google search said they are supposed to be transparent about it. The woman at desk mumbled that it was cancelled due to maintenance. Almost like she didn’t want to tell us. She said the reason our flight was going to be so far away was because there’s five of us. She said they could separate us, but it’s literally like one flight here and there over the next three days and we have small children so we can’t separate. She said all the flights were full because of the cancelled flight. She said there’s nothing they could do and that they can’t offer to put us on another flight because with a different company because they don’t have commercial partnership. We have since decided to rent a car and drive home. It’s Sunday now, and we’ve already started driving home, but we haven’t called yet to get the refund or compensation because yesterday was just so stressful.

My questions are: How should we word that we want to be compensated? And how much could we be compensated?