Fulton is dead weight and has to go after the second test. He is simply not up to it. I'd give Rutherford a bit more time as he is younger and still learning.
Basically the key areas we are lacking are: Opening batsmen, a spinner, a keeper batsman (not essential but becoming more and more common in intl cricket, and more and more important in tests)
We have some depth there, as you have rightly pointed out martinb. We still don't have true balance.