In the previous version of the conflict, the Houthi's had a fairly steady supply of food aid coming into Hodeidah, that is mostly gone. Also they got supplied by air from Iran. That is also down to a trickle. I would say grabbing the ports will be key to limiting the Houthi's ability to attack. They will have a dwindling supply of drones and missiles. Going into the mountains to fight them would be a fools errand with the KSA army, the Houthi make good light infantry.
KSA and UAE need to bury the hatchet and work together again to support and build up the Yemen government. At the very least don't work at cross purposes. Egypt has a competent army (comparatively) and with the two Mistrals would be a valuable asset to taking and holding the ports. As I have said at the same time offer money and food to the tribes to turn on the Houthis. That is the way hostilities traditional seem to work there. The Houthi will be short of money, food and weapons which will cause support to fade. Ensuring no aircraft can fly in to Houthi territory is also important. Once the Ports are seized, the Yemen army can push up and clear North along the coast to Mocha, which is the another port and has a airport. It is currently held by Tareq Saleh who is independent, but aligned with the Yemen government against the Houthi. From Mocha to Hodeidah is 147km. In the last conflict, anti-Houthi forces reached the southern edge of Hodeidah from this direction.
KSA forces can slowly push south to take Al luhayyah which is one of the key smuggling ports for the Houthi. The next target is Al Khawban, another large fishing/smuggling port and further south is Ibn Abbas. The port of Salif would also be an important target. Which looking at AIS seem to be very valuable to the Houthis and should be blockaded. Once the port is to be taken, if from the sea, the only road to it can be cut, preventing the Houthi's from reinforcing it.
Making sure the Yemen government can supply aid to the towns they capture will be key in gaining support, the west need to bump up aid to the Yemenis government (yes I know they are corrupt) Aid should be mostly in the form of goods for now, then as an area stabilizes, then rebuilding of wells, clinics, etc.
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