We use the Xxxx's mummy option or the person's name but I think that you have to go along with this person's choice, really, if that's what she wants. My ds is married to an American Jewish girl and from the time I've spent in the US they are very polite. No one uses 'Sir' or 'Madam' in the UK now but I hear it regularly there, plus older people are often addressed as Mr/Mrs/Miss X.
Slightly to one side, as my children have reached their teens their friends seem to get all embarrassed to use first names so we suddenly become Mr&Mrs. Although having said that, dd1's closest friends have started calling dh and me Mummy and Daddy!!! I can be out somewhere minding my own business when I'll hear a loud MUMMMMMMEEEEEEEEEEE and it'll be one of the teenage hobbits.