Odds are you can stabilize it enough by using an axle nut on the outside.
However the problem is very simple --- the axle is too long. More specifically the built up spacer stack on the right is too high. Remove the outer locknut and the remover will sit flush against the freewheel.
BTW- the freewheel seems to be pretty far inboard. Is this a narrow hub to which you added spacers for a wide frame, or is something else going on?
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