Limited war is always a tricky topic. Where do you draw the line between a full on war and making the seas safe for trade,
Luckily, the aftermath of the Vietnam War gave us an answer. The War Powers Act. Which gives the president authority to use the military in situations exactly like this. If he tries to turn it into a big thing, then it has to go in front of Congress.
The Houthis took up arms because of Iranian backing and Yemeni local politics. The Western countries aren't solving that any time soon. And they're already receiving HA.
That's not what they're doing. They're firing at any ship they believe even has a Western financial stake in it. No matter where it's going or what it's carrying. It could be taking Italian tractors to Somalia to encourage local farming as part of an aid program and they would fire at it.