Activity, especially weight bearing is needed to maintain bone strength with or without a joint replacement. But after a total hip, the load and compression from activity becomes even more important.
This is because the implant itself changes the force and direction of load through the bone. The effect is called stress shielding. Studies show that the shape and density of the bone can even change as a result of stress shielding. Bone loss can occur, which would be a problem if your mother ever needed further surgery on that hip.
In general, there are so many health benefits from activity your mother should be encouraged to resume former activities and regain more function. She may need some help in this area. Perhaps there is an exercise group she could attend. Or maybe a membership at a local health club or YMCA would get her going in the right direction.