She told me her mother is a doctor.

Literal

She [topic-は] [own mother [topic-は] doctor is] [quotative-と] me [to-に] said.

彼女は frames the matrix speaker, while the embedded clause 自分の母は医者だ has its own internal topic 自分の母 — two distinct topics operating at different levels. The plain copula だ inside the quote is typical of indirect-style reporting. 自分の母 is a third-person way to say 'her own mother' that fits narrative; in everyday first-person speech a Japanese speaker would more often say うちの母 ('the mother of my household').