Translation:My sister has taken my horse which I did not like.
"Som" can only refer to the horse here, so it means you didn't like the horse. There's no ambiguity in the Danish sentence, unlike in the English. If you wanted to say you didn't like your sister taking it, then you'd have to say something like "og det kunne jeg ikke lide (at hun gjorde)".
So, in English the word should be"that" instead of"which". "That" points to the horse, "which" points to the action of the sister. And I cannot explain why.
Without context, I think it could be either, much like the English translation.
Does this mean "My sister has taken my (sole) horse; and I did not like that horse," or "My sister has taken that one of my (many) horses which I did not like?"