change checkbox checked property via other elements in Redux form

I need to used Redux form to build a form composed of two columns in a dialog. The left column is a list of checkboxes. When I check on one item, the checked item shows up on the right column. If I uncheck the item on the left, the according item on the right column disappears. These can all be achieved by redux form by now. However, items on the right column are need to be clickable. When the item on the right column get clicked, it should disappear, and the according item on the left column should be uncheck.

What I have done is to use state to control items show and disappear on the right column. However, if I uncheck the item on the left via clicking the the according item on the right, the actual submitted data will still include the unchecked item. Also, the according checkbox on the left column still stays checked.

Does anyone knows what should I do to control items on the left column via items on the right column? Thanks in advance.