Can you cast a stealth spell on a vehicle?

This is his DM.

No, you may not cast Pass Without a Trace on a sandship that is not specifically outfitting for stealthy movement. Especially since stealth sand ships exist.

I think it is worth taking this one back to first principles (PHB p.6):

How to Play

1. The DM describes the environment.

2. The players describe what they want to do.

3. The DM narrates the results of the adventurers’ actions.

The environment consists of a desert and a boat-like vehicle. The players want to hide its tracks.

The PHB (p. 183) has this to say about tracking:

Track. A character can follow the tracks of another creature, making a Wisdom (Survival) check when the DM calls for it. (The Dungeon Master’s Guide has rules for tracking.)

And the referred to DMG info is on p. 254:

Adventurers sometimes choose their path by following the tracks of other creatures - or other creatures might track the adventurers! To track, one or more creatures must succeed on a Wisdom (Survival) check.

Now, if you want to take an absurd RAW position, no one can track the boat-like vehicle because it is not a creature and only creatures can be tracked. QED.

Assuming that you are going to be more sensible than this, you have to accept that "creatures" has to include their mechanical or magical mode of transportation. If that is how you want to interpret it then there is no reason that Pass without Trace won't do exactly what it says it will do:

For the duration, each creature you choose within 30 feet of you (including you) has a +10 bonus to Dexterity (Stealth) checks and can’t be tracked except by magical means. A creature that receives this bonus leaves behind no tracks or other traces of its passage.

Providing that each creature on the boat-like vehicle is within the area of effect (30 foot of you) then I see no reason why it wouldn't work exactly as advertised. After all, it expends at least a 2nd level spell slot per hour and is a Concentration spell so its not without cost to the caster.

From a pure realism point of view there is nothing to stop characters from mechanically erasing the tracks of the vehicle providing they are willing to spend the time, effort and have the necessary skill (Dexterity (Stealth) or Wisdom (Survival): use your best judgement). All the spell does is cause this to happen through magic.

Yes, conceivably

You can conceal a vehicle's tracks with magic, especially if the spell can be cast on an object.

Your question specifically asks whether magic can help a vehicle "to hide its tracks" which is maybe not what folks think of when they see "stealth." This answers the question specifically about making it harder for pursuers to follow your vehicle's tracks.

Don't make tracks

You don't mention the size of the boat, but if it's small enough (like, a canoe) you could cast Levitate on the boat, and poll it along like a Venetian gondola. But the boat can't weigh more than 500 lbs, so unless your party is the gnome squad you might need to split up.

Spells that can cover your tracks with weather events

The 8th level spell Control Weather could conjure up rain or wind to expunge your tracks.

The 2nd level spell Gust of Wind or the 3rd level spell Wind Wall could blow the tracks away for short periods (they only last a minute). But might be handy in key situations.