Also, In my own opionion, i think you should send photos to nanna.
Im sure she knows what her son is like, and if she is any kind of woman she will want to know her grandchild regardless of her opinion toward the mother of that child.
Half the time in these situations the granny doesnt even know she has a grandchild out there.
If she doesnt want anything to do with the baby atleast you done your bit, you have gave them the ball and it will be up to them what they do with it, atleast then at the end of the day you know you have done all you can