Sounds like you have either the front end or backend (or both) going through a toe angle change accelerating versus decelerating. Typically when one end or the other goes toe out, and it doesn't take much at higher speeds, does a car feel squirrely. The change in pitch - nose up/rear down under acceleration or nose down/ rear up under deceleration - is the cause of the toe change. It may take some experimentation to determine which end is changing.
Other factors can be the tire pressures, the shock rebound settings, camber angle or even the front castor angle can contribute to this type of problem. Make small changes and see if it gets better or worse.