I can’t see a single goof in your post.
It is usual for an active CG (compulsive gambler) to deny they are gambling even when there is more concrete proof than you have because lying is symptomatic of the addiction. In my opinion, you have done the right thing for your whole family, including your wife, by protecting your paycheck. You are right that it won’t stop her gambling but it does make it harder for her to find the wherewithal to indulge her addiction.
It is difficult for the non-CG to understand that money is not the root of the problem – it is the actual gamble that causes all the tension, misery, lies and deceits. Giving money to a CG is the same as giving a drink to an alcoholic – it is only a means to an end.
Unfortunately without treatment the addiction gets worse and if your wife continues she may find herself in debt and think that you will bail her out. Clearing the gambling debts for a CG also clears away their worry leaving them free to continue unabated and I think maybe you could give this some thought before it occurs.
It is possible that you wife is unaware of the support that is available for her should she want to control the addiction that is over-powering her at the moment. I believe it is good to print off the ‘Gamblers Anonymous 20 questions’ and give them to the CG – sometimes it helps for them to realise that what they are experiencing is not unknown. Your wife will have low self-esteem and little confidence as her addiction means she will feel failure over and over again. Arguing, pleading, threatening has little effect as she is unable to think logically or reasonably about her addiction, hence the need for the right support. We have an excellent helpline on this site, run by CGs who are in control of their addiction and a dedicated counsellor who would be able to offer your wife a light at the end of the tunnel that sadly you cannot shine for her. We also offer CG only groups and a CG forum where she would be welcome – CGs do not fool each other. Perhaps you could also get the address of the GA (gamblers anonymous) group in your area for face to face support.
You may well be thinking as you read this that I have not listened – your wife is saying that she is not gambling so why would she seek support? The point is that ‘she’ knows she is gambling and although she cannot admit her addiction to you, it is possible that she knows she needs help. I suggest leaving information where she can see it and she can read it in her own time. It might be that she screws it up and throws it in the bin but I have heard of CGs who have retrieved information they have discarded once they have had time to think.
It is important that you look after yourself and your children while their mother is not taking responsibility. In my view it is important to get as much knowledge as possible of the addiction because knowledge will give you power over it and help you cope.
I fully appreciate that there will be more things going on than you have written in this first post as I really do know how difficult it is to live with this addiction casting a shadow on your life.
Keep posting – you will always be heard