Your mother may be a candidate for the new mini-incision method of joint replacement. Instead of a long incision with trauma to the muscles, only a four or five inch incision is made. It's not always necessary to cut the muscles with the mini-approach. There's usually less blood loss as well.
There are several factors to consider here. How well can your mother follow directions? Even with the minimally invasive surgery, there will be a few guidelines to follow. After surgery, rehab is very important so she will need to be able to complete her exercises correctly every day.
How's her overall health otherwise? Her age and the condition of her bones may be other factors to consider. Studies show mental status does affect outcome. A specific study on patients with Alzheimer's having joint replacement hasn't been done yet.
Talk to your mother's doctor about this decision. There may be some other medical information that can be helpful in making this decision.