When talking to a mother (whom you would siezen) and her child which one would you use?
Waren Sie beide in der Stadt?
or
Wart Ihr beide in der Stadt?
Or is it uncommon to address several people at the same time when you would "duzen" some of them and "siezen" the others?
Several possibilities there:
You can ask the child in a cutesy tone (Duzen), if it's a rather young child. The mother will probably smile from ear to ear and wait for the kid to answer, or eventually answer the question for her kid (or call the police for harassment ;)
If the kid is your friend (similar age, same school, etc. etc.), you can just quickly greet the mother (Siezen) and talk to your friend as usual.
If you only want to talk to the mother, you would address her with "Sie" and pretty much ignore the child.
So basically, you address everyone individually as appropriate. If you want to talk to the group as a whole and there is a clear difference in authority (such as parent and child), you usually talk to the person "in charge" according to the usual rules of Duzen/Siezen.
If you would address each person in the group the same as an individual, then addressing the group that way is appropriate as well.
Examples: You would usually "siezen" a traveling group of pensioners, and usually "duzen" a group of teens or younger, depending on circumstances.
I'd prefer the first. The second would also address the mother with "Du".
Addressing several people at the same time is not uncommon. I'd err on the more formal side.
I support @Hackworth's answer as a general solution but want to add that there are areas in Germany where the people are very relaxed and switch to "du" quickly or use it instantly, for instance the Rhine-Ruhr area, Dortmund, Essen, Bochum. It's very common to use "du" with a total stranger there.
In the quite common situation that you are friend/colleague with someone, but not their partner, a typical solution would be to address your friend with:
Willst du und dein Mann mit uns zum Flughafen mitfahren?
There is no really correct way to adress everyone at once which is one reason that in groups there is a very strong tendency to equalize the use of du and Sie.
In very formal speeches or invitiations, people will actually use both forms.
To the mother:
Waren Sie mit ihr in der Stadt?
Waren Sie beide in der Stadt?
If you address the mother with your eyes, both are perfectly valid.
To the daughter:
Warst Du mit ihr in der Stadt?
Wart Ihr beide in der Stadt?
Possible, if you look at the child. It seems respectless towards the mother, but depending on the circumstances, it needn't be.
What's not possible: to talk to them simultaneously. If you want to make a distinction between 'Du' and 'Sie', you have to decide to whom you talk. You cannot make a difference and no difference at the same time.
