Dear Tripped Up,

Last September, my husband and I left our kids with their grandparents and set off to Ireland. Our $2,132 itinerary took us from Minneapolis to Toronto to Dublin on tickets booked on United Airlines through Expedia but ultimately operated by Air Canada, a United partner. We had boarded our connecting flight in Toronto (and I was already dozing in my seat) when the captain announced an operator had crashed the jet bridge into the starboard engine. We were given hotel vouchers and told we would be rebooked for the next day. Checkout time came and went without a word, so we went to the airport and were told to call Air Canada customer service. An agent booked us a flight for that evening, and we printed out boarding passes at an airport kiosk. But when we tried to board, we were told the boarding passes were invalid. Eventually, we were offered two options for the next day: Fly to Dublin via Newark, or return to Minneapolis. We cut our losses and went home after staying the night in Toronto at a hotel. But United refunded us only $1,087, barely half of what we paid. Air Canada did reimburse us for the second hotel and other expenses, but we believe the airlines owe us not only a full refund, but also 400 Canadian each ($295 apiece) under Canadian law for denied boarding. Both refused. Can you help? Michelle, Edina, Minn.

Dear Michelle,

I found the 58-page dossier you sent along with your story to be quite convincing. (It also convinced me that either you or your husband is a lawyer, which turns out to be true.)

I skipped over Expedia, since your trip had already started, and reached out to United and Air Canada — as you flew on an airline’s partner, it’s a code share arrangement. A spokeswoman for United, Erin Jankowski, quickly sent me a statement noting that the refund you received from United was as per Air Canada’s instructions and referred all other questions to it.

Air Canada, on the other hand, took almost two weeks to get back to me, and its response was underwhelming.

“Our records indicate these customers were not denied boarding in Toronto,” wrote Peter Fitzpatrick, a spokesman for the airline. “Instead, it appears that following the cancellation of their original flight to Ireland they opted to return to Minneapolis from Toronto rather than go to Dublin following the delay. Once that was identified, we did rebook the customers on a flight back to Minneapolis.”

No compensation, no word on the $1,045 still missing from your refund and no explanation as to how you were turned away at the gate for your second flight and yet “not denied boarding.”

Air Canada did offer you and your husband a credit worth 1,200 Canadian dollars toward a future flight, Mr. Fitzpatrick wrote to me, “to account for the impact on their travel plans and experience.”

There was no response to my direct question asking why your boarding passes did not work the second night. In fact, it isn’t even clear from Mr. Fitzpatrick’s initial statement that Air Canada believed you even tried to board, despite the boarding passes you included in the dossier sent to me and the two airlines.

I wrote back with more pointed questions, thanks to what I learned after reading up on the Canadian Transportation Agency’s air passenger protection regulations and speaking with Tom Oommen, the director general of the C.T.A.’s Analysis and Outreach Branch.

“We have what I would call a very complete holistic system of consumer protection for airlines,” he said. For example, when flight disruptions occur for reasons within an airline’s control and the airline cannot get passengers onto another of its own flights within nine hours, it must book the passenger on any airline, including competitors it does not have agreements with, a requirement that the United States does not impose.

Mr. Oommen also noted that if a passenger is stuck midway through a trip and is not happy with the options to continue on, the airline must offer to rebook that passenger “on a flight back to their point of origin free of charge and refund their entire ticket.”

He wouldn’t specifically comment on your case, but that is exactly what happened to you. (The only exception to these rules is when the disruption is not within the airline’s control, Mr. Oommen said, but when a mechanical problem is caused by an airline employee or contractor, “it’s hard to make that argument.”)

There are also many circumstances in which Canada requires airlines to compensate passengers — between 400 and 2,400 dollars — for flight delays, cancellations and denied boarding within the airline’s control. There is an exception for when such issues have safety implications, which could apply to the first night’s engine damage, but not, it seems to me, for the second night’s nonfunctioning boarding passes. That sounds a lot like denied boarding.

This time, you heard back before I did, and forwarded me several emails from Air Canada, including one that said the carrier had approved a cash payment of 400 dollars per traveler. Then Mr. Fitzpatrick emailed me to say you would receive a full refund.

So you got what you asked for, but of course you would rather have gone to Ireland. And what happened, exactly, when Air Canada refused to board you in Toronto? Mr. Fitzpatrick told me United had canceled your ticket before you even got to the gate.

I found that confusing — the boarding pass bears an Air Canada ticket number, and you had not even spoken to United that day. So I got back in touch with United’s Ms. Jankowski, who looked into the situation further and found that “United canceled the tickets after sending messages to the operating carrier, Air Canada, informing them that the tickets had not been properly reissued to the rescheduled flight.”

Apparently, somewhere in the interfacing bowels of the two carriers’ systems, your Air Canada boarding pass was invalidated by United, and neither airline contacted you. And that’s too bad, because Mr. Fitzpatrick later confirmed that second flight left with empty seats.

When you decided to just go home, the Air Canada representative at the airport said you had to call United. The process to untangle the mess and get you booked on a flight back to Minneapolis required hours and six different United customer service representatives and supervisors.

Your experience is a good reason for all of us to avoid code shares unless they are necessary — such as when an itinerary includes flights operated by different airlines.

All this because you originally booked Air Canada flights as United code shares — a choice you found on Expedia. When I recently ran a Minneapolis-to-Dublin search on Expedia for a week in April, the first two choices that appeared were the same route via Toronto with no price difference, one booked directly on Air Canada and the other as a code share on United. Assuming you saw the same thing last year, I bet that if you had booked the Air Canada choice, you would have made it to Ireland, albeit a day late. All the more reason to book directly, with one airline.

There is one final mystery: Why wouldn’t Air Canada admit this was a case of denied boarding, and follow the required C.T.A. regulations? Yes, your case doesn’t precisely fit the agency’s official definition, which is written to describe overbooking or changes in aircraft, but if an airline erroneously cancels a passenger’s ticket after it has already printed a boarding pass, and you are stopped at the gate, what is that?

I presented this as a theoretical situation to the Mr. Oommen of the C.T.A.

“Classic denied boarding is what you’re describing,” he said.

That means you could file for an additional 400 dollars each for this second incident, and put that toward a new flight to Ireland — say, on Aer Lingus, direct or through Chicago.

If you need advice about a best-laid travel plan that went awry, send an email to TrippedUp@nytimes.com.