RE: If we feel weak, we might think that we need to engage in wars, overthrow other governments. If we are strong, we don't have to.
Except this has not been the case at all. It's been the exact opposite as what you state. The U.S. has been a military superpower for many decades, and nevertheless has been engaged in near perpetual war of one degree or another for those many decades. The U.S.'s neighbors are Canada and Mexico--neither of which have ever been even marginally close to being a military threat. To the east and west, the U.S. is guarded by vast oceans. A foreign soldier has not set foot on U.S. soil for like 200 years. The only 'attacks on the U.S.' have occurred within foreign nations, or have been perpetrated by terrorist organizations as a result of our presence in foreign nations. We have enough firepower to blow up the world like 12 times over. Strength, or power, is not something the U.S. has been lacking, militarily.
So no, peace, quite clearly, does not necessarily follow from strength at all.