Mrs. Kate Smith.
I think it should be Mr and Mrs John Smith and Miss Kim Smith, otherwise it sounds like John is their surname.
Dr. and Mrs. John Smith, or Dr. John Smith and Mrs. Ann Smith. John and Ann Smith is also appropriate, and might be the best choice in this situation.
The proper form of address would be Mrs. John Brown. To differentiate her from other Mrs. John Browns, she would be identified as Mrs. John Brown née Smith.
* Proper address for a General and his wife: General & Mrs. John Smith.
It can be two ways (an individual choice): Mr. & Mrs. John Smith or John and Joanne Smith
Dr. Smith and Mr. Smith separately..
She still is a Mrs. The women I know who have kept their names use the Mrs. with their own name. So, if she is Kate Smith and marries she becomes Mrs. Kate Smith.
Mrs Smith, unless she has specifically changed her surname back to her maiden name
Captain Edward.J.Smith
Mr. John Smith and Mrs. Jane Doe or Mr. and Mrs. John Smith Either would be correct, though the latter appears more formal and less cumbersome.
Addressing a Mayor and his wife: Mayor & Mrs. John Smith
Dr. and Mr. Smith.