In this scenario, context would be used to differentiate the two. There really isn't a way to decide between ihre as their and ihre as her. In fact, if it weren't written down, you would equally be able to say that sentence translates to "you are taking your clothes from me." If I were speaking and what I was trying to say was ambiguous, I would phrase the sentence like this: Sie nehmen von mir Katjas Kleidungen.

In this scenario, context would be used to differentiate the two. There really isn't a way to decide between ihre as their and ihre as her. In fact, if it weren't written down, you would equally be able to say that sentence translates to "you are taking your clothes from me." If I were speaking and what I was trying to say was ambiguous, I would phrase the sentence like this: Sie nehmen von mir Katjas Kleidung. In other words, being more specific would solve your problem.