。
When she realized mother wasn't angry, her eyes lit up with joy.
Literal
Mother [subject-が] is-not-angry [nominalizer-のを] knew and, she [gen-の] eyes [topic-は] joy [with-で] shone.
Two notable pieces. (1) のを知る ('to learn that X,' 'to realize that X') nominalizes the subordinate clause with の and marks it as the object of 知る. Distinct from ことを知る, which feels slightly more formal or general. (2) で here is 'because of' or 'with' — the means/cause by which the eyes shone. 輝く ('shine, sparkle') is a literary verb, often used for eyes, stars, or things gleaming with light or feeling.