My brother has no children was always invited to parties, football matches, important other events like communions etc. Also just for dinner or a visit because he has a relationship with me, DH and his nephews.
He always attended, loved and treated my boys well. He used to take them to football games on his own. My sister had a daughter, he would take her out independently.
My boys loved and still love him. He was their mad uncle, who'd come round (just for a visit) chase them round the house, make them scream with laughter and have boundless energy with them.
It never occurred that he wouldn't want to be fully involved with their lives, he loved it! The boys are adults now and still go to the odd game of football together. Buy presents etc for each other.
As for your mum looking after the GC, as others have said this would be a day of total happiness and an escape from the stress she is suffering. Small children have that power to cheer.
On a practical note, what can you get put in place for respite for your mum and to help your DGM? Could you do a few hours with DGM whilst DM had the children?
And your DB is rude and BVU!