how can i presude my mom that i can ショップ at hot topic

Be an adult and have a mature, civil conversation with her. Let her explain her reasoning for not letting あなた ショップ and, calmly and intelligently, explain why あなた think あなた should be allowed to ショップ there.

hmm if your parents dont let あなた ショップ there they may have a good F-ing reason