For example, if in English I say
"That makes me feel better"
"Me" is the direct object as it relates to "makes," but then it is the subject as it relates to "feel." I don't know if there is a grammatical term for this kind of sentence.
I can't figure out how this should work in German, and don't really know the right search terms to figure it out by googling. The direct way would be
"Das macht mich besser fühlen"
But that really doesn't seem right to me. I've tried typing in forms of this sentence into dict.cc to see if I can find a similar phrase, and everything seems to come up with other ways of constructing the sentence that get around this. Perhaps it is just not a valid construction in German? Maybe this sentence would need to be translated
"Deshalb fühle ich besser"