The girl whose mother is sick is absent today.

Literal

Mother [subject-が] sick that girl [topic-は] today absent-[ongoing-ている]

母親が病気のその少女 — a relative clause where が marks the subject within the clause: 'the girl whose mother is sick.' This is the pattern where が (not は) appears inside relative clauses. 欠席している = 'is absent' (ongoing state).