The mother was startled to hear that and immediately felt sympathy.
Literal
Mother [topic-は] that [object-を] heard-[sequential-て] was-startled-[sequential-て], immediately sympathized-[completive-てしまった]
Three chained て-forms: 聞いて → びっくりして → 同情してしまった. ~てしまう marks the sympathy as involuntary — it overtook her before she could help it. すぐさま = 'immediately' (more emphatic than すぐ).