Of course the whole purpose of etiquette is not to cause offence. It is about being polite and curteous.
So to my elderly (female) relatives I would always address the letter (if it was just to them) as Mrs John Smith. They look for it, and it makes them happy to see it, so I do it.
To my younger friends I would always do Mrs Jane Brown (except my cousin who I would do the former, as she does to me as it makes us laugh.)
If an elderly lady is widowed she should continue to be address as Mrs John Smith. If she is divorced she can (if she wishes) keep Smith, but would revert to her name ie. Mrs Jane Smith.
When writing to the Queen you should address the letter to Her Majesty The Queen.
You should begin the letter
Madam
With my humble duty.........
Letters to the Queen should end
I have the honour to be, Madam,
Your Majesty's most humble and obedient servant.
So there you are, just for future reference.