Oh this is a tough one. I think you may be better leaving your daughter with relatives or friends in the UK for the 3 months so as not to disrupt her schooling rather than having her try to integrate into a totally different school system (Greek) in a language that she doesn't know. If she came to Canada, at least there is a good chance that her schooling would be in English, unless you are going to Quebec!
Children do not necessarily appreciate change, but in my opinion, I think she should come with you. The 'always wanted to live in Cyprus' may be true, but she's probably never lived there long term, just on holiday with you, and it would be opening a far nastier can of worms to let her 'leave' you for her grandparents than for her to remain with you and go to Canada. My son didn't want to come to France when his dad got a job there, but there was no question of him doing anything else. The family moves together. You may have to harden your heart, and 'make' her come, because at 13 she is still a minor and under her parents' legal responsibilities. But I do appreciate that it could signal a very rough period for you all.
And how do your parents feel about having a teenager (with all their good and bad points) living with them? It may not be all sunshine!
GOOD LUCK IN WHATEVER YOU DECIDE.