Sorry to read your situation, I can not magine what you are going through.
You should compile all evidences e.g. his messages to other women, his messages to you which clearly shows ignorance. Also, you should put together the evidence of conversation with him regarding immigration.. But you shouldn't have left Canada, Cuba is a great country but the protection you and your child could get in Canada will be umatched. Also, if you are able to provide all the evidences, he won't get a custody of the child.
It sounds like he used you for immigrating to Canada. You should talk to IRCC also tell them the whole story, tell them that you were not aware that he is using you for immigration. Perhaps, you will be required to provide the evidences and witnesses (if any). Hopefully things get better for you soon!