Westjet knew we would miss our connection. No staff at Laguardia to handle rebooking. Very inexperienced Gate Agent, with no authority. She had to call operations and get approval for every ask and rebooking. We stood in line for over 2 hours waiting to be rebooked and was then told they had no options. After I pressed they agreed to book with a different carrier but could not transfer luggage. When we arrived for our new flight, it was cancelled with no notice. Both carriers, American and WestJet argued over who was responsible. Finally American rebooked us to Charlotte, with a 4 hour layover and then home. Very disappointed with Westjet and will not use them again. Root cause was their inbound crew from Laguardia to Toronto was late and had to change planes. They had to clear customs in Canada and then through US customs before we could board the aircraft, which had been in Toronto for hours. WestJet gate agents in Toronto knew many would miss their connections but refused to rebook or help at all.