I'm so sorry for you, OP. You sound really lost and bewildered. I wish, wish, wish that my Mum had had access to a place like Mumsnet all those years ago because she was second-guessing her decisions.
One tip... make absolutely certain that your husband has no replacement bank cards hidden away or due to arrive by post - to your home or elsewhere. My father made a big performance of 'handing over' his bank cards knowing that the new ones had been safely squirrelled away. His 'need' to gamble overrode every decency, every concern for his wife and young children. His wants mattered more. That is the mind of a gambler and that is the mind of your husband.
I think he's realised that if he wants to stay in the family home he has to agree to whatever you say but, be under no illusions, he will be thinking of ways to thwart your attempts to stop him gambling. That is absolutely at odds with his addiction which will be working harder, much harder than you can, to get him back to it - and it will win because it is what he wants.
Only when he has hit rock bottom and there is no more leeway for him to gamble, when there is every reason to genuinely choose recovery and find his way back to his family, is there hope. He is not there; he is not nearly there.
I realise that reading these posts is jolting for you and make very unpleasant reading. There's no way around that because this is a serious subject and I guarantee that you do not know everything or even nearly everything... how could you? Your husband left you in the dark about the extent of his gambling. This is who he is. He has shown you. You want to believe the best of him because you love him but, he is not the man you believe he is and, if he were honest and able to look at himself with any clarity, he would agree with that.
I will offer that your husband may be a 'nice guy' underneath but think of him as a zombie for now. He has no mind of his own, he is an addict and until he stops being an addict, he will continue to lie and cheat and take from his family.
Never mind what he says, look at what he does.
What you do next really, really matters.
Get support from your family, they will want to help you. Let them do that. They have nothing to gain but the best for you and your children, to make sure that you and they are safe. The best thing that could happen to your husband is that he hits rock bottom, hard and fast. That can't happen whilst he's living with you and your children in the family home, it really can't.
I'm sorry for what I'm writing to you, I don't know you, but I'm earnest about your situation because I was the child of a gambler. Our lives were blighted by him, we had so little money and my Mum worried herself sick all the time. That is what is on the horizon for your children if you focus too far on your husband and his needs. He is an adult. Your children need you so, so much.
Please call out for support, but not from him. He is elsewhere and you cannot reach him right now, maybe never again. An addict services themselves first. Always first.
Your children, your house and your family money... protect those at ALL costs. 