Both are correct, but mean slightly different things.
I highly recommend Dave —> to represent you in Korea with your software.
I would use this in a context where it is established that you need someone to represent you, and it is just a matter of figuring out who. So, this sentence is saying that it is Dave who I recommend.
I highly recommend (that) —> Dave represent you in Korea with your software.
This one could be used in the context I described above, but also when there are many possible courses of action — it may not be established that you should have someone represent you. So, this sentence is saying "Dave representing you" is what I recommend.