How do I force my dog and cat to respect each other?

I recently saw an episode of My Cat From Hell with Jackson Galaxy. In this ep, a couple moved in together and each brought their older cats who hated each other. To get them used to each other, he had the owners feed them on opposite sides of a closed door. They could smell each other, but not see or hurt each other. After eating at the same time with a closed door no longer caused any reaction in either cat, he cracked the door between them. As each step was tolerated with no reaction, the door was opened further. Once the door was open, they moved the dishes closer to each other. With lots of time and positive reinforcement, the cats could be trusted to be in each other’s company without drawing blood.

I also second the recommendations to work on obedience with the terrier.

Or get some weird artists and psychics to stitch a giant alien squid together and then crash it into the living room.

I would let them fight it out until dominance is established.