I live in Florida, but I think the information I am about to give is accurate. To be safe, double check what I say.
You should be able to sell to anyone within the state of Michigan without anything special, although I don't know any quirks Michigan may have when it comes to gun laws.
You can transport the guns across state lines without any problems and no special permits needed. To be on the safe side you do not want them in ready reach. To play it real safe, have the guns in the trunk and unloaded with any ammo in another area of the car.
www.packing.org is a real good resource I consult anytime I travel out of state.
As far as selling a fire arm to someone in another state, you will need to have a dealer with a Federal license ship the weapon to another dealer in the buyer's state that also has a Federal license. Any gun shop will likely do it for you for a small fee. Likewise, the buyer should be able to find a gun dealer in his state to accept the weapon for a small fee.
No gun can be shipped by the postal service, UPS or Fed Ex is fine. If you were not selling the gun but only shipping it to a relative or such, that to the best of your knowledge does not have any restrictions to having the gun, you could bring it to UPS and be just fine. The sale part makes it not so easy.
Double check what I'm telling you with a gun shop close to where your Mom lives. The gun shops know the laws better than the cops