It's simply not appropriate to use a card for a milestone whether its a birthday, wedding, funeral or whatever to insert some other topic that is unrelated.
Putting that check in a birthday card would be just as wrong. It's not that its confusing its that its inappropriate. It's mixing a business relationship with a business relationship.
And I will comment on the background that was provided about uncle and the other siblings not being involved in grandma's care. That is their choice to make. They are adults and cannot be coerced to do something they don't want to do. Expecting them to do it is not reasonable.
In fact, there are certain situations where I could see a sibling staying as far away from a situation like that as possible. It seems that the OPs parents were grandma's point people. Under those circumstances, I could see the OPs mom using that position to insist that uncle do all sorts of things--I make that judgement on the slim but rather significant faux pas of her being condescending in the wedding card.
She could be deigning to speak for this man's mother because she was around her more in her last days and that not only us not fair, its rude.
It also could have been taken as a criticism--"she would have wanted you to have this".... <and unspoken> "even tho you did nothing in her last years to deserve it."
I know what its like to have family members decide for you what your contribution to a parent's care should be. There is already enough complicated emotions going on with the illness and death of a parent without one's sister or brother in law complicating it with expectations.
As to the OPs parents taking care of the estate: also their choice to take it on. Just because someone names you as an executor doesn't mean you have to serve. Also, in most cases even family members that serve as executors may be paid for their services.
So, I really don't have all that much sympathy for the OPs parents. They made their choices in choosing to visit her every day and to disperse the will. Other adults made different choices.
Neither side has any right to criticize the other as to those choices. If uncle had wanted to be an executor he could have pursued that.
The thing that bothers me the most about this is that this mother is sharing all of this with the OP. Also, an email reducing you to tears because it takes you to task over your rudeness? Oh well, grow up. Her response doesn't mean that he was rude.
This is, after all, a mother who negatively characterizes the uncle's very justifiable criticism of the OPs very rude behavior in not acknowleging gifts that he sent.