I'm guessing that the Danish language does not have verb form of "trust". In English I'm guessing you have a similar situation with the word "faith". You can "have faith in someone", but you can't say "you faith someone".
In english you "trust in someone", in danish you 'put your trust' on someone.
Why is 'He trusts not in her' or 'He doesn't trust in her' incorrect? It is both a literal translation and correct in English.
Sometimes an exact literal translation isn't the best translation. The first example is very awkward phrasing and wouldn't be used in modern English. For using "trust in her," one would say, "I don't put my trust in her."