。
Her daughter is her pride.
Literal
She [topic-は] her own daughter [subject-が] pride is.
Both 彼女は and 自分の娘が contribute to the topic-subject split — 彼女は marks the matrix topic ('as for her'), and 自分の娘が marks the within-frame subject ('her daughter is the pride'). 誇り is a noun ('pride, source of pride'), and the construction [X]は[Y]が[noun]である reads as 'as for X, Y is the noun' — a classic 'X has [a quality] in/about Y' frame. Slightly more elevated and definitive than 娘を誇りに思っている.