Try thinking about "pulling" with the bottom hand to accelerate the barrel in a arc. Keep the arms locked into the shoulder rotation (use the abs/torso) at the start of the swing.
It sounds like you're muscling up the top hand to push forward (which can cause a hitch, delay bat acceleration). Keep the top hand/arm relaxed and firm up the front arm (take the slack out, slightly lock the front elbow). Any loading or pulling back with the top hand will pull the linkage a little tighter and keep the arms/shoulders connected as a unit.
Think "Pull" first and then push. The top hand is not the power hand, the body pulls the bat around in an arc. The lead arm pull is where the power is for initiating the swing. Both the pull/push are important just don't push first.
Batting cages can cause many timing problems. Pitching machine don't have the same "Visual stimulus" as a pitcher. Striding to early will make you reload (hitch). Try to start your stride ,"anticipate", as/after the ball leaves the machine. The swing should be continuous process without a break in the process (hitch, reloading, striding early, over loading).
Don't try to time the ball going into the machine, or somebody dropping the ball into the pitching machine.
Chances are you will not have the same problem against live pitching.
And always swing the bat in an ARC.
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