Hione,
Bottom line:
If you are considering suing anyone for your losses due to the airline refusing to board you on the Cuba flight, you will need to engage a lawyer. I suggest you take everything you have here and speak with a lawyer. You may have to do some research to find a lawyer with expertise in these matters. This is not a "routine" legal issue.
Then, listen to that expert legal advice, make an informed decision and go forward.
No one on this thread has identified themselves as a lawyer licensed in Canada. I am certainly not, either.