Your brother is a TWAT, sorry if that offends you but he is showing no consideration at all.
Is the other granny moaning that she does most of the chilcare and your mum has it easy.
Does your Mum have hobbies that could fill a free day a week such as swimming, walking, kepp-fit etc? If not encourage her to get one so she can have a day to herself without a demanding child on her hands. A child who may well miss his nursery friends.
When I worked I hated the fact I was out everyday and missing out on things to do for me. I had 2 DC's at home so I was either working or mothering. If I was near retirement age I would definitely want a ME day.