Does the divorce take effect with the صيغة I uttered, given that I don't recall the exact wording of the phrase "if she travels," and whether the intention was "alone" or "without me"? And must I prevent my wife from traveling altogether or only to her family? Or should I treat the divorce as contingent only on her traveling "without me," especially since she has traveled with me several times, and there were two previous divorces?

If it is highly probable that you intended to prevent your wife from traveling without you, then your oath is restricted by that intention, whether you explicitly stated the restriction or left it general. The one suffering from waswasa (obsessive whispering) who pronounces divorce, whether immediately effective or contingent, due to waswasa, their divorce does not take effect. And whoever doubts whether they pronounced divorce or not, or doubts whether they divorced willingly or due to waswasa, their divorce does not take effect; because the original state is the continuation of the marriage. One must disregard these waswas and not pay any attention to them.