Having had good sized TC in the 90s on a long bed truck along with a larger Saint Bernard, he did just fine in there.
When you talk about removing the dinette, I assume you're talking about the seats also? If so, where are you going to sit or eat?
You also have to consider with an older larger dog that is hard to lift, how are you going to get it into the TC if it has or develops mobility problems?
Since it doesn't sound like you own a truck or TC yet, don't consider a short bed truck. Actually, I think you should look at a smaller Class C. It will have a lower entry and more room.
Bill