It doesn't help that I lost my mum when she was 35 and I was 14
There you have it in your own words. In your own experience, you recognise how special the bond is between mother and daughter. That's exactly what your DIL is experiencing and demonstrating . She is a new mother and turns to her own mother. You missed that; but they have it.
So, stop feeling it's any personal slight against you; it isn't. It's just natural, especially when the baby is so new/ young. You WILL get to babysit him in just a short time.
As he grows, and his character and nature emerge, each grandmother and each grandfather will develop their own unique relationship with him. It's not a popularity contest.
We are the paternal GP's . Your time will come, as ours has.