You can’t disentangle the two like that. If you posit that the first gulf war was justified, you’re 90% of the way to justifying the second. The intelligence was that Iraq was rearming. If your position is that the U.S. would’ve had to intervene in the event Iraq invaded a neighbor again, then it doesn’t seem unreasonable to invade preemptively to avoid a potentially costlier conflict.
But yes, the first time it was Iraq that was the belligerent and invaded Kuwait.