She blew up when she saw her husband walking with another woman.

Literal

Husband [subject-が] different woman [with-と] is-walking [nominalizer-の] [object-を] saw [and-て] she [topic-は] flared-up.

かっとなる means 'to flare up / lose one's temper suddenly.' ~のを見て nominalizes what was seen and marks it as the trigger. 別の女 = 'another woman.'