My mom is in a nursing home and has frequent urinary incontinence. What is causing this and who should I get to treat this?

Check for infection. One of the reasons elderly patients may develop acute urinary incontinence is urinary tract infection; prostate problems( in men), bladder problems( hyperactive bladder) , neurological problems, hydrocephalus ( normal pressure hydrocephalus) etc...
Many things... Many conditions can cause urinary incontinence in patients in the nursing home environment. Actual documentation of the frequency and extent is important. Urinary tract infections, stress incontinence, medication side effects, primary neurologic disorders, or even normal pressure hydrocephalus can be causal. It may be best to have her visit (or be visited by) her primary care physician.
See below. She may be evaluated by an urologist but it is very rare to have one come to a nursing home and it is risky to take your mom out to one.  i recommend using a provider such as silvercare solutions who actually can bring a provider to your mom in the center and evaluate her bedside.  she may need a vaginal support device, an overactive bladder medicine that is not contraindicated.
Time to See a Doctor. There are many reasons for an elderly man or woman to have urinary incontinence. They may have stress incontinence, urge incontinence, mixed incontinence, and even overflow incontinence due to a number of age-related chnages as well as medical issues. Incontinence in the elderly may also be due to medications (e.g. Diuretics) or due to limited mobility. You doctor will do the evaluation.
Bladder incont. She may be evaluated by an urologist to try determine the cause. Treatment options are not too good. Most elderly end up wearing diapers or with an inserted foley catheter. Medicines cause a lot of dryness may affect narrow angle glaucoma or worsen bladder retention.