First and foremost, you cannot transfer a loan to someone else. Just not possible. Second, unless you go through the application process and get approved for a new loan by yourself, you can't remove a cosigner.
Now that we have that out of the way, please understand that if your mother in law wants to buy the car, she needs to get approved for a loan in her name only. The rate her credit qualifies her for is the rate she will get. Not sure if she can do this, though, as you said that she "has paid off her house, paid off her other car and wants another", but also said "does not have any credit to get her own loan". Either way, the rate you and the cosigner got, and the "super cheap payments" that stem from that rate are completely and totally irrelevant. Her credit will dictate her rate.
Your vehicle will need to be paid off in full, so that the title can be transferred. If she can't get approved for the total amount owed, then your mother in law will have to pay the remainder out of pocket, up front. Again, you cannot transfer the title with a lien on it.
If you're thinking that you might let her drive the car and make the payments, don't. First, all legal liability is still yours. The registration will still be in your name, and she cannot obtain insurance for it, as she has no "insurable interest" in the car. Also, it is highly unlikely that you would be approved for a second auto loan without the first one being paid off. Having her make the payments while being the sole operator is considered subletting, and is strictly forbidden in your contract. They can repossess your vehicle for this. In addition, if she's in an accident, the insurance company can refuse to cover it. There are no benefits to this.
20 years retail auto sales experience.