Is it Okay to Install a Regular Battery Inside the Coach?

The best advice is to get a vented box if you are going to do that.

The battery in my TCer was located under a bench seat and unvented when I bought it and was still there when I sold it with no problems but venting is highly recommended.

My concern would be if you have gone through that many batteries will another one make it through the trip or will you fry it, if you fry it under the seat with no venting then you will have issues. I would stay with the one battery till you get home.