Liquid Vinyl

Vinyl responds to thermal welding techniques. Is that how it is assembled, perhaps?

The vinyl you speak of is generally applied (without seams etc) by dipping into or coating using a solution of PVC, either a plastisol (PVC dissolved in plasticizers) or an organisol (PVC dissolved in solvent). Talk to one of the major PVC manufacturers or simply refer to an encyclopedic , Google, etc. Slush-molded PVC boots etc are typical applications. The plastisol or organisol is solidified generally by heating. Dyes can also be added to the solution etc.

I'm wondering if you are talking about a two step molding process where the foam core is inserted in a mould and the 'vinyl' cover is injected to surround it?

Can you provide a web link that shows such a seat?

most of the seats for boats are formed by vacuum forming a heated vinyl sheet into a mold and letting it cool and take the shape

the cover is then either glued to or urethane foamed behind and then edge wrapped and stapled etc.

Polaris and the industry are moving toward urethane spayed skins which are more durable and more resistant to cold in the case of ski mobiles

if you are trying to repair a hole or tear plastisol can be used

look up vinylpro.com

good luck