Unless Canadian family courts are very different from American ones you are not in a pleasant ride. Custody battles are ugly and all the cards are stacked against the dad. Not saying you can't win but if this actually goes to court expect her to say more then she does 90% of the child care. The goal will become to prove the other is unfit to have custody. I would push hard for mediation if I were you and get her to agree to something reasonable and if you don't have a lawyer get one now and be prepared to spend a gross amount of money in fight you will probably lose. Just having a lawyer will put you in a better position negotiate. Unless she has access to a large amount of money the cost of a custody battle may convince her to be fairer to you.

Sorry to sound so grim but it is a grim situation.