Hi Magclin,
It sounds like your wife is in a similar situation to where my family were in the end. The was no reason for them to believe a word I said. They had heard all my lies and broken promises before. Even when I meant those promises the addiction was too strong so I broke them anyway.
That’s why actions are important. The actions that will help you stop gambling, like getting banned, posting here, going to GA meetings etc are the same actions that might give your wife cause to think “Hey, maybe he means it this time”
Have you shown your wife this site? She can get support and advice for herself in the Friends and Family forum. She would also see soem of the success stories here and see that there is light at the end of the tunnel with those positive actions.
Keep posting and let us know what actions you are taking.