I don't want to be putting words in your mouth or thoughts in your head, but it seems to me that this is why you want a divorce. He changed your lives completely, abdicating his responsibility as husband, provider, and father. And he is happy with the way things are. He will not consider changing his life from the way it is now. What is good for him is not good for you. And when you try to make things better for you, he rejects it.
I don't know anything about the laws in Greece, but I hope that they are favorable to divorced women. Your kids need you as the primary caregiver. Your H has nothing to give (at least not in terms of time or emotion). What would he do if he had custody and the kids were sick for a week? He is not flexible enough to care for children. They need you to be primary custodian with him providing financial support.