Any ideas to ensure that my dog doesnt chew our hot tub cover?

I don't understand why it's so difficult for you to just put the dog in a kennel? Unless you already had it made up in your mind that you were going to get rid of the dog and this is just your excuse to do it. It's very simple to crate several of us here have multiple dogs and do it all the time. If you do re-home I wouldn't take her to a shelter. I would at least try and find a loving and responsible home for her. If she doesn't have papers I would have her spayed before I re-homed her so that she couldn't be bred if she is not already altered.