Start by not using words like "whining" -- this may create tension and show your disapproval.
Recognize that the son's behavior seems appropriate for a much younger child, or one with many emotional needs. With Mom as his sole source of attention, love, and security, he must fear a loss or change in that status. Address the boy's needs and you will find that he can build a positive relationship with his mother on much stronger ground.
Plan a balanced schedule for the times the three of you are all together. Allow for some time when you and your partner are both focused on him; some time when he is solely with his mother; some time alone with you; and some time when he must be by himself.
Recognize that every newly emerging family experiences these situations and that prevention is easier than correction. If you are serious about your family relationship, seek the help of a counselor to begin planning for your future. If you hope your situation will get better or just go away, you could be allowing troublesome behaviors to become deeply resistant to change. Seeking my objective advice is a great sign that you already have a good method for problem-solving. Good luck.