Well, after reading the post and all the comments, it kind of gives me an impression that this is happening to you Naweed sahab. Secondly, the other party wants him to loose his job so that they can say in the court that since he has no job so he can't take care of the child and no court would give custody of a child to a jobless man. Thirdly, if the official address was misused then there is no justification of it since not misused by an employee of the company for some matter related to office but his personal life. At work there are situations when we share our passwords with colleagues as well but that's all official so that can be explained.
I don't have an idea if its that easy to hack into an email account unless the password is known to someone. Key logger is one way to log everything you do on a computer that's why I never log into my email addresses at work, never, only from my personal computer at home. I have one master/primary email and all emails/accounts are bind to it and that email is unknown to most. Design your own strategy, compromising your email is not child's play, there can be serious consequences of that.