Well, only on harder acceleration at medium to high speeds could be one of the motor mounts (with about a dozen different names), like the lower one on the passenger side and below the alternator.
A weak strut could allow this to happen, but not very likely at the higher speed, that usually shows up in tire wear.
Last thing would be an attaching point that has cracked and the heavier acceleration gives it the reason to wobble, witness marks at the connections and cracks should help identify why the engine/trans is shifting, or a half shaft is getting out of alignment and causing the wobble.
A weak strut could allow this to happen, but not very likely at the higher speed, that usually shows up in tire wear.
Last thing would be an attaching point that has cracked and the heavier acceleration gives it the reason to wobble, witness marks at the connections and cracks should help identify why the engine/trans is shifting, or a half shaft is getting out of alignment and causing the wobble.