The best thing you can do is get on a plane. You need to see your mother with your own eyes. There's no substitute for seeing firsthand how the facility is treating your mom and reviewing her daily medical records. Visiting has another benefit: the presence of family members personalizes your mother to the staff and shows that she has loved ones who are looking out for her. You may find that a simple visit resolves the problem. If no family member can go, the next best option is to hire a local advocate, such as a care manager, to check in with your mom.
Keep in mind that most likely you'll be dealing with neglect and not intentional abuse. Nursing homes are often understaffed, and the aides may be overworked and undertrained. When you visit, keep an eye out for signs of neglect, such as pressure sores, dehydration, weight loss, or poor hygiene. Pressure sores generally appear on the buttocks, shoulder blades, and ankles when someone's been left in one place for long periods of time. Of course, pressure sores aren't a sure sign of neglect, they're just a red flag.
If she has experienced out-and-out abuse, your mother may appear reluctant to interact with staff or fearful of her care providers. She may have bruises or injuries.
In addition to your on-site visit, do a little homework. Medicare's nursing home comparison website is a great resource to find out about a nursing home's history of complaints. You can also check with the state agencies that oversee nursing home licensing -- every facility should have records on quality and complaints.
If the evidence suggests abuse or neglect, you can file a complaint with your local Long Term Care Ombudsman or Adult Protective Services agency (find your local Adult Protective Services agency, which will investigate). In some states, you can also file a report with the attorney general, who deals with Medicaid fraud control.
If it appears to be a clear situation of abuse, you should absolutely move your mother right away. If she's on Medicaid, though, finding another placement can be very tricky because of the shortage of beds. You'll have more nursing home options if you have available funds. You can also hire in-home care for your mother in her own house, if she still has one, or in your home. The important thing is to get her out.