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Let's try and do some math with this. Will use Wikipedia for numbers. Gravity at Pluto's surface: 0.61711215789 $m/s^2$ Gravity from Charon- Pluto's near side- 0.0002724276 $m/s^2$ Gravity from Charon- Pluto's far side- 0.00027242753 $m/s^2$ Centripetal Acceleration- Near side- 0.00001749536 $m/s^2$ Centripetal Acceleration- Far side- 0.00006647414 $m/s^2$ ...


I am not aware of any particular standard for the primary body, however for the Pluto system, in this image the 0,0 point is on the opposite side of the hearth: And in this image, the hearth is shown to also be at the opposite side from Charon. So I assume you are right.

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