Would it be possible to have two people riding one entity? (Only one would control the vehicle, the other just sits in there.)

Short: Yes

 

Longer: Making Player move on server side only (since normally it's done also on client) might cause some laggy-movements on client, since server will be making your client player move.

I believe Flans mod accomplishes this. Maybe check their github?

I think one approach might be as follows. When second player is mounted, the RenderPlayerEvent would render that player as you want in the vehicle (while cancelling normal rendering). The rendering would use exact position based on the vehicle to avoid lag issues that Ernio mentions. But you would still also keep the positions up to date on both client and server. You'd also have to intercept the second player's input to avoid it trying to control player position while mounted.

How would I make the second rider mount my vehicle and become a second riddenBy entity?

Just think dude.

Entity has 2 Entity fields - riddenByEntity and riddingEntity. There is a method that is being called every tick.

public void updateRiderPosition()
    {
        if (this.riddenByEntity != null)
        {
            this.riddenByEntity.setPosition(this.posX, this.posY + this.getMountedYOffset() + this.riddenByEntity.getYOffset(), this.posZ);
        }
    }

 

This is called somewhere around update methods.

 

What you need is it inside your own MyEntity.class ass 3rd Entity field - "passenger" or something and every tick update his position. To make all smooth you will need to read some vanilla - there is a good deal going on there - don't forget NBTs, resetting states (nulling) and all that shit.