This is the cole rollen freehub.
The freehub is shot as it has some lateral play which means the gear jumps from high to low to high.
I have no idea how to take this puppy apart.
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Easy peazy. There are two, perhaps three reasons why this freehub could have developed play.
1) Wear on the aluminium axle where the bearings seat.
2) Very worn bearings
3) Bad bearing preload adjustent. This is very unlikely since very few hubs have preload adjusters for cartridge bearings.
To remove the freehub, remove the end cap where your allen key is inserted at the moment. You may have to insert another allen key into the other side to lever against.
Once the cap is off, everything slides off towards the right hand side of the axle. The bearings may resist, but they are only press-fit on and some gentle knocking will get them off. There will be at least two bearings inside the freehub. The right-most one will appear to be impossible to remove. It isn't. Just jam a screwdriver past that bearing and lever the sleeve behind it out of position. That sleeve looks like a continuous smooth pipe inside, but it is only held in place by the axle that's now out.
Lever the sleeve to one side and drift the bearing out from the left side of the freehub by inserting a pin punch and catching the inside ridge of the bearing. Tap alternative sides until the bearing pops out. You may have to devise a bit of a jig to get it to come out fully because if the freehub is face down on a flat surface, the bearing cannot come out. The open jaws of a vice is good enough.
Now that the right side bearing is out, peer inside and see what retains the left bearing. It could be nothing or it could be a circlip. Remove and drift that bearing out to the right as well.
Inspect the axle for wear. Replace if necessary otherwise it will still wobble with new bearings.
That freehub is made either by Novatek or DT Swiss, who makes plenty of OEM freehubs. The pawls are standard and the pawl spring which usually rusts away, can be made from 0.5mm piano wire much quickly than you can say "mail order".
The red seal is pretty standard on may Novatek/DT hubs and yours seems just fine.
Fix that wheel, don't discard it.