Translation:They do not want to go without her coming along.
Maybe it is easier if you think of it as '[uten at] + [hun kommer]', i.e. the 'at' belongs to 'uten' more than to 'hun'. Literally 'without that she comes along'
It's the same in German: As we do not have a gerund -ing form such as English, we use a subordinate clause.
Instead of 'uten at', how about 'med mindre' (unless). Is that a less common usage?
in portuguese we have the same structure as uten at - "sem que" - but it's followed by subjunctive verb.
They're comparable to the difference between goes and go:
He goes. (Han går.)
He wants to go. (Han vil gå.)
There's no mention of "outside" in the Norwegian sentence. For all we know, they could already be outside.
I said: They don't want to go except if she goes with them. And it's wrong?
I'm not sure if it fots the norwegiab but 'except' is a bit awkward here in english. 'Unless' works better