I don't think you can do exactly that. I don't have your same cameras though. I don't think I can click the remote once to focus and then click again again to shoot as you described. If mine do that, I'm not sure how to set that up. I'll describe what I do get and maybe that will help. This is on my d7x00's.....but i do still have questions on how to use this thing. the button can only be pressed once at a time - first for focus, second for release (no half way down, just all the way down). what if i want to do what i did with the old one which was focus first (holding release just like regular shutter) then rip off a series of shots without refocusing?
If I am in a release priority mode, I get an instant shot, no focus. But I can focus with the camera. In my case I use BBF, so I pre-focus with the back button, then shoot with the remote. This works for me for pretty much everything. You could set af-c, release priority without using bbf. I think its the defaualt for af-c anyway.
If I am in a focus priority mode (default for af-s), clicking the remote once will initiate focus and shoot all with one click. In that case, I get focus every shot. Usually not what I want, so I stick with af-c, release priority which is my setting for bbf anyway.
Another thing I learned. In af-s, focus priority, it works as I said above, but with one twist: If I go ahead and prefocus with a half press of the shutter, that apparently tells the remote not to focus on the rest of the shots. This might work for you if your camera behaves the same way.
In any case, I don't think you can shoot a burst. You will need to keep pressing the button.
Here is an old thread:
https://nikonites.com/d7000/12901-continuos-shooting-wireless-remote.html#axzz4omhvXFOQ