Takako wanted to cancel the wedding because she thought that Okami would not let Enishing inherit the inn if they were to marry. Her comments when Okami gave her the ring indicate so.

I think the reason Okami said what she did about Enishi inheriting the inn is because she intends to close it down. At the beginning of the episode, Okami was discussing something with Denroku. I think it is about the impossibility of keeping the inn afloat.