I'm not too bothered about my parents sharing any dx with their friends and wider family tbh. It's nothing to be ashamed of.
I'm slightly weirded out by your formal email requesting details of the letter concerning your child's confidential diagnosis etc. it's the sort of thing you'd bollock the local authority for, rightly, if you hadn't signed a release of info waiver, but in all honestly, what's wrong with calling him and saying 'bloody hell, dad, what did you tell Aunty Jo?'
I think you might have over-reacted, I'm sorry. A lot of people use their Christmas correspondence to let folk know about important things happening in their lives - and I think it's somehow quite sweet that he has understood the importance of the dx and how important it is to you, and this 'unholy breach of confidentiality' demonstrates how much it means to him, as well. I did lol at you not receiving a copy. Does he's end you a copy of every letter he sends? (Do you have this problem with the LA as well?) 
Why are you keeping the dx a secret? It's mildly ironic that that was his initial instinct, and one you had the hump about, but you are now upset about him Not keeping a secret...
It'll be fine. Call him and apologise for your ridiculously formal email, and then just have a chat. Really. He probably thought the was being supportive by acknowledging his Gus's disability, and that it showed he was recognising him as a member of his family, inclusive, and that he has nothing to be ashamed about.
I'd be more worried about a grandparent NOT talking about the gc's in a Christmas email, tbh. Or gp's that refused to acknowledge a disability and hid it from their friends.
This sort of attitude is why kids with sn get the whispers behinds hands treatment when they rock up to school, and why parents of kids with disabilities feel unable to talk about it. Why shouldn't he discuss his gc? Why should he hide the disability?
This sort of stuff needs normalising, not more parents who think they shouldn't tell. The great elephant in the room.
Yes, two out of three of my kids have additional needs. I'm a lot further down the road than you are bough, and I'm well over the secrecy aspect.