It would help your son if you and his grandmother were on the same page, so to speak, about this. It's understandable that young children will sometimes want to go into the parents' (or grandparents') room when they wake up at night. But, the best approach is to disallow this, and to patiently and supportively guide the child back to his bed. It's not helpful to him to frame his behavior as 'acting like a baby'. Try to be sensitive to how he views the situation, and be gentle and patient, not rejecting, as you set limits on the behavior. It sounds like the basic problem concerns the relationship between you and your mother, and hopefully the two of you can come together on a sensible plan for the sake of your son.
sit down and talk to your mom about this. explain to her that it is not fair, and that your other child is feeling left out. maybe she will listen and if not keep trying.