Would talk back to her also be an acceptable translation?
I wouldn't say so. To talk back to someone doesn't necessarily mean that one is contradicting them.
Could you use modsige here and is there a difference?
As far as I know, "at sige hende imod" is the same as "at modsige hende". I have searched several sources and have found no indication of there being a difference.
Why isn't "how dare they contradict her?" acceptable?
Turde is past tense. Present tense would be tør.
I'm not sure if "How dared they contradict her?" is acceptable in English, though.
So basically you are saying, How dare they speak against her?