I married a widowed physician (retired)
Wow, he managed to retire young. Anyhow, personally, I think you were wrong for sending a message and "signing" his name. What's to stop you from doing something worse next time the two of you have an argument? Not saying you would do that, but what if..... How would you feel if he had done something like that to you?
To me what it boils down to is
I agree with BL, I don't think it was right of you to send the email and signing his name to it.
If he bought two tickets and planned to bring you along, I don't see how he intended to keep you a secret. It seems more likely that he preferred to introduce you in person when he was there. His reaction to the letter seems a bit over-exaggerated, but not anything I would consider a good idea to pick a fight over.
He seems like a man who is used to very traditional gender roles. It makes sense that a guy like that would prefer to marry who would fill the traditional female role when he remarried. I don't know if I would call that substituting the old wife. It seems more like just being an old-fashioned guy. Some women would be okay with this, and some wouldn't.
"I am not an equal partner in the relationship -- partly because he has a lot of money and I don't -- and never will be, but I've accepted that in order to be married at all after being divorced a very long time."
These are the sorts of things you should have been considering years ago before you married him rather than now.