Wheatpenny's suggestion will work in general: turn on IK on the one hand
for each kid, then parent those hands to the ends of the rope.   But it really
depends on how the rope is built.  It will need to have pivots on each handle,
and you'll need to make those pivots rotate opposite to the rope itself.
(Sort of like pedalling a bicycle...)

May be a lot easier to leave parenting out entirely, and carefully adjust
every frame so the rope and both arms stay together and in rhythm.

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