I think the fact that the driveway is there is almost irrelevant. I would saw cut at the property line and put a chalk joint in. I would tell a bank that its not your driveway, because theoretically its not. But "we're using it because the owner hasn't said not to."
At the end of the day its not your driveway, If it is on someone else property, i wouldn't even break it up. The only thing you can do is saw cut the concrete at the property line. If you did break it, you may end up in a lawsuit for breaking it.
I would look at it for what it is. My neighbors driveway. Negotiate concrete and saw cut money from the seller. Install the car port in the front. When the owner of the adjacent property comes, he can do what he wants with it.
I bought a property with a fence in the wrong location. I know it when i bought the property. My neighbor never say anything about it. He sold the house last year. The new owner went nuts, but he also know the fence was in the wrong location when he bought his property. I told him if he want to move the fence, he had my permission, but i wanted a surveyor the set the marks. He never moved the fence, he didn't want to spend the money. The fact that i didn't argue with him satisfied his ego.
We are professional investors, it is our job to deal with and correct these types of issues. That is why we can buy at a discount and sell at retail. (or barrow at retail numbers.
I hope you don't pass on this deal for this issue. Speak with your attorney about what I have written here. I think he may agree.
Good luck!!