。
She wept with grief over the death of her child.
Literal
She [topic-は] own child [of-の] death [in/at-に] sadden [then-て] cried.
我が子 is a faintly literary phrasing of 'my (own) child,' more weighty than the everyday 自分の子. The に on 死に here marks the trigger or cause of the emotion — the standard pattern ~に悲しむ ('be saddened by ~') uses に for the object of feeling, just like ~に喜ぶ, ~に怒る. Then 悲しんで is the て-form of 悲しむ ('to grieve') connecting to 泣いた ('cried'); the て-link reads as 'and (so),' giving 'grieved and wept' in unbroken flow. The whole sentence has the elevated register you'd expect for a description of profound loss.