Lazzaroo you haven't done anything wrong.
I have known someone for years now, since I was fourteen, and only found out yesterday that his name is really James. He is known as Seamus, which I think is the Gaelic for the name James, but everyone thought Seamus was his actual, official name. I think this sort of thing happens more often than anybody realises.
I also know a whole family who give their eldest boy the first name Graham but refer to them all by a different middle name, because actually calling them all Graham in conversation would be confusing apparently. So the friend I knew as Stephen, and his father who I knew as John, were actually Graham Stephen and Graham John. I'd known them ten years before I found that out and even some members of their own family were surprised to find out about the Graham part.
As I said, families can be strange with names, and I don't think you've done anything wrong by not checking the spellings. At least this way, you haven't had to choose between the two, you've picked the spelling you prefer without anyone being able to accuse you of preferring one Nan above the other and your daughter has a beautiful name spelled just the way you and your partner like.
About the note. It's hard to say without reading it, but I think it sounds nit-picky for no good reason. But I would let it go and perhaps when your daughter is older and you tell her why you chose her name you can tell her that one Great-Nan used a different spelling as an interesting twist to the story.
I think I'd be interested in that if I were her. But you can make it a fun addition to the story rather than a nit-picky one.
I just realised my Great-Grandma was known as Minnie, but my dad has no idea what her full name was. Minerva? Wilhelmina? Something else? I love the name Minnie, but there's nobody left to ask who might know her full name.