Yeah, I see this a lot in a bunch of lessons. "Together" is superfluous. It's not used in English this way. "Please let me go with you" is what an English speaker would say. Or, something like "Please, let's go together." "Together" and "with" don't mix well.
I agree with much of the above. If I heard someone say, "Please let me go together with you." I would be confused. I would probably think they meant to say, "please let US go together with you" and I would be looking for the other person they are talking about.