Hi Beth. Hope I am not butting in. If your mom has not done so, tell her to get photos of her rash. It is important documentation. Have her place something near it, like a coin or ruler, before photographing to give it size definition.
From what I understand, six weeks of the proper dose antibiotic is the minimum treatment for an infection caught within two weeks of the bite. If the infection is longer, longer treatment is needed. If symptoms are still present, further treatment is needed. Doxy is often prescribed first because it can be effective for Lyme and it treats Ehrlichiosis.
I believe the recommended dose of Doxy for Lyme is 300-600 mg daily with 400 mg daily often prescribed. I believe the recommended minimum dose of Amoxicillin for Lyme is 3000 mg daily. Dr. Burrascano lists the recommended doses starting on page 18 in his treatment guidelines at http://www.ilads.org/lyme_disease/B_guidelines_12_17_08.pdf