My father absolutely refused to let me go to college.
Literal
Father [topic-は] I [subject-が] university [toward-へ] go thing [object-を] no-matter-what permit-try [contrast-は] did-not.
どうしても~(よう)としなかった means 'absolutely wouldn't try to.' The volitional 許そう + とする + は(contrastive) + しなかった stacks three patterns: volitional attempt, contrastive negation, and past negative. The は intensifies the refusal.