I think that the third panel is a pun of some kind, but in the end I'm still not really sure why Orin and Okuu begin fighting.

I think when Rin said ghostly car Okuu though ghostly things are old and broken(like ghostships are always old and broken down) thus a ragged car

Kefit said:
I think that the third panel is a pun of some kind, but in the end I'm still not really sure why Orin and Okuu begin fighting.

It (the ghost carriage) is also a Kasha (what Rin is suppoed to be). In some stories, they are demon cats (like Rin) and in other they are ghost carriages with huge human faces on the front that drag you itno them and cart you off to hell.