Translation:The girl calls her mother and she saves her.
in english to call is a transitive verb, therefore it does not need a preposition. to call someone, the girl calls her mom. The danish construction is different and independent from the english one, so you can't translate -til- literally because it's not gramatically correct in english.
I don't see anything grammatically wrong with "The girl calls to her mother." It subtly shades the meaning and removes the possibility that she is calling by phone, but other than that it means essentially the same thing and certainly doesn't have anything wrong with it grammatically as an English sentence.
I think the meaning changes quite a bit though. In Danish ringer implies that the calling is done through a phone and in English you can't call to someone on the phone. So in this context I think "to call" should be used as a transitive verb in English, while in Danish ringer needs the preposition till. Prepositions don't make sense is the short answer :)