Mine was also marked as a duplicate of this one even though the issue I am having is the EXACT opposite of what original poster put.
I see my skin and I see other player's skins just fine but both other player son LAN see my skin as Steve. Marking mine as duplicate doesn't solve the issue either.
Only thing I've learned so far is it MIGHT be a skin server bug but that's it. v. disappointed.
Example of bug. 1st view is from host side, 2nd view is from guest player's side on LAN.