Velas Vallarta Resort Timeshare review: Time share purchase that was cancelled but not refunded

We purchased a timeshare at Velas Vallarta Resort on 11/30/2020. we had put down $4000 down on 2 different credit cards. We decided it wasn't a good time financially so we went back the next day (12/1/2020) and cancelled it. They made us write a letter and sign it (which we did). I requested a copy and they said I didn't need one. I started to take a picture of the letter and they snatched it away. I had a bad feeling at that moment but they then came back and said we were all set and we would get a refund on our credit cards with in 15 business days. When we got back to the US we called our credit card company and told them what happened and that a credit should be coming. It never did. We then called them many times. We have spoken with their legal dept. also (one of the people we spoke with when we went in to cancel said they were from the legal dept.). Later when we spoke with them they said they never received the letter. They kept lowering the price trying to get us to keep the Timeshare. We told them we just want to cancel. Now they are saying we can't. We feel completely scammed. They are telling us we will have to hire a lawyer and we will still lose. They said no matter what we do we are stuck with it. Right now we are screwed out of the $4000. We are trying to fight it through the credit card but we don't have a copy of the cancellation letter because they snatched it away before I could even get a picture of it. We just want to cancel the purchase and get our $4000 back. We have even tried to contact someone higher up thinking this has to be a mistake but no one will let us. We feel trapped. I hope this isn't the way they do business.