"And international law is about preventing a country from invading another; that's why the principle of sovereign state is so important (and old)."

You somehow seem to have forgotten that Saddam invaded Kuwait. This is a critical aspect that if you forget or ignore, you can't possibly understand the situation. It was Saddam's invasion of Kuwait which caused the members of the UN Security Council to make the decision to take action. It was precisely this violation of international law that Bush senior decided he would not allow to be violated. United States *could* have taken the position that it wasn't in the US national interest overturn "the facts on ground" which resulted from Saddam's invasion.

Afterall the Arab countries in region just prior to the invasion, had inform the US that this was an Arab matter and that any intervention by America was not welcome. It was only after Saddam had actually used miltary force on his Arab brothers AND that Saddam was seen as a threat to Saudi Arabia, that suddenly America was generally welcomed to take steps to intervene. Normally speaking, the US can be counted on to defend an ally which we have security arrangements with. For instance we will defend S Korea- we might even use nukes to defend it if deemed neccessary. The same goes for Taiwan. But also part of this is, we expect that we will have a place at the table in order to take actions to aviod potential miltary conflicts.
Had Saudi Arabia not had strong connections to US, had Saudi Arabia not been a critical country in terms of national security [mainly in terms of global security {vast oil reserves and Mecca for a billion or so Muslims], and had Saudi Arabia not felt threaten by Iraq, the US could have easily stayed on the sidelines and let the Arabs resolved this situation in whatever manner they thought best. To put it bluntly, Kuwait by itself was not a global security issue, but it was "protected" by international law as a nation state.
And you have the vision of the New World Order:

"We stand today at a unique and extraordinary moment. The crisis in the Persian Gulf, as grave as it is, also offers a rare opportunity to move toward an historic period of cooperation. Out of these troubled times, our fifth objective -- a new world order -- can emerge: a new era -- freer from the threat of terror, stronger in the pursuit of justice, and more secure in the quest for peace. An era in which the nations of the world, East and West, North and South, can prosper and live in harmony. A hundred generations have searched for this elusive path to peace, while a thousand wars raged across the span of human endeavor. Today that new world is struggling to be born, a world quite different from the one we've known. A world where the rule of law supplants the rule of the jungle. A world in which nations recognize the shared responsibility for freedom and justice. A world where the strong respect the rights of the weak. This is the vision that I shared with President Gorbachev in Helsinki. He and other leaders from Europe, the Gulf, and around the world understand that how we manage this crisis today could shape the future for generations to come.
http://www.sweetliberty.org/issues/war/bushsr.htm

George Herbert Walker Bush had the idea of strenghtening the UN and thereby international law. The cold war had ended. We could get back to idea of bring about global peace- instead having Cold War considerations overriding our actions. This why he pushed to have this a UN involved and was why his son also continue to at least try to get the UN involved [in the end the UN security council failed to stay the course].

ANYHOW. The whole point was that Iraq did not follow the cease fire agreement which resulted from the Gulf war. Omit the Gulf war and the cease fire agreement reached, and there is no valid reason why the US would use miltary power to force compliance to some vaque idea that some countries should not have WMD [this includes long range missiles, chemical and biological weapons, and nuclear weapons as the term is defined by and in accordance to the cease fire agreement].