Hotel express *******

I joined hotel on the 26 on sat i was told it would take 72 hours to process because it was a weekend.I sent an email on Monday 9am to cancel membership.I sent emails for 5 days with the consult sending me pillar to post.I had not received a card or anything.I only received a welcome email on the 29th after I asked to cancel.Now they tell me my refund will take 4 to 8 weeks because the membership was already processed how when they said 72 hours and they only sent an email 29th.can someone do due diligence as I have all the proof.I expect my refund to be processed and definitely not in 4weeks