OK.. We are buying my mother-in-laws home, is it possible for us to be added to their deed and refinancing the house in our name, and then paying them for the house. Pay off their mortgage and whatever. If so would we be able to have their names taken off the deed once it's been financed in our name or would they be "partial owners" of our home? Or is any of that even legal to begin with? (The interest rate is lower if we refinance it in our name and we don't have to put anything down)

Can you be added, yes, can you take them off latter, no, not unless they will sign them off. So if things go bad, and they decided not to.
Also they would be getting the tax benefit not you.

You can do a contract for deed, your name is not added to the deed, but you have a contract to pay a certain paymnet for so many years, after you have done that, they agree to sign over the deed to you. You than have a written contract.