Hi Rosegold,
Just a wee bit of info on German accents over letters, in case it might be of help in the future.

As you probably know, umlauts are used in German:
ä &
ü.
If you are unable to type an umlaut, just add an "e" after the letter, i.e.:
ae,
ue.
To avoid "u" and "n" getting confused (in German script, this is possible), writers used to add a horizontal stroke above a "u". This was sometimes straight, sometimes almost half round.
Some writers still do this today, but it is becoming less popular. (As is actually writing using a pen, unfortunately...

)
The thing is, people do not usually use the stroke above a "u" when signing their names. It is not normally a constituent of a signature. (There are, however, always exceptions to rules.

)
I am therefore wondering whether Barbara's maiden name was actually Müth, because an umlaut is used in a signature if it contains a letter (or letters) which actually have an umlaut.
(I hope you can follow me! I know what I mean, but it is a bit tricky to explain it.)
I just wanted to mention this in case you are researching Barbara and are hitting brick walls. If that happens, try looking for
Müth or
Mueth.
Best regards,
Karen