A state of hostilities existed between the US -- coalition if you want to call it that -- tempered only by a cease-fire.
It was hostilities sanctioned by the UN, which made it acceptable. The US, on its own, is not allowed to invade Iraq because Iraq invaded Kuwait. The UNSC decides that, not the US.
The UN Resolution clearly states the use of force as an option for noncompliance. The US also included language in the ceasefire agreement that it reserved the right to act on its own.
I don't see in the text where the US "reserved the right to act on its own". Where is that?
Clearly, the US had more than enough legal authority to resume hostilities considering the number of times Saddam violated the terms of the ceasefire agreement.
12 years later? Nothing clear about that at all.