This is a completely normal situation that stems from the bond between the mother and the baby. It would be abnormal if this did not happen. The baby is eager to share the POSITIVE or negative experiences he has had throughout the day with his mother. His first reaction when he sees her may be to cry, not because he has been unhappy all day, but because the feelings he wants to share with his mother are too big and he cannot control them. That's all.
The situation seems difficult for the grandmother as well. She had a lot of fun with her granddaughter all day long, but her daughter couldn't witness it. She actually did a good job.
This is normal and mine is the same, he could be fine at nursery or with my mum but then whinges with me. Even if he’s playing with his dad then I come downstairs he starts clinging to me and whinging even though he was fine and happy before I come into the room. It’s very annoying but it’s because you are their safe person that they feel they can let their emotions out to
Tell your mother to grow up and get over it. Its a child that has a variety of feelings and closer attachments to you than to their grandparents. Its not rocket science. Why are boomers like this?!??!