Even though I know it would be fair, I cannot say if it would be rash for you to tell your mother that you want to split all the household bills between the two of you. I cannot tell you what to do – I can only support you so that ultimately you will be able to make informed decisions about what is right for you. I believe the ability to know what to do comes with knowledge of the addiction.
The answer to your question will always lie with you. ‘If’ you had the conversation you suggest, would she listen or understand? It is unlikely she would do either if her addiction is active. Have you thought through the consequences of her answer? Threats and ultimatums with someone with an active addiction are, in my view, a waste of energy. Unless you have fully thought through what you will do if/when she does not keep her side of the bargain, then I suggest you don’t make the suggestion – yet. Every time you make a threat or an ultimatum which you cannot carry through, her addiction will see it as a weakness on your part.
Do you have a good relationship with your father? Is he aware of your concerns? If your father does not live in the home then it seems to me that him having a fit, if she reneges on her debt, is not nearly as bad as the misery and fear that this situation is causing you, his daughter. If your dad has opted out of responsibility to his wife, leaving you to feel like the surrogate spouse then, in my opinion, you have a right to demand support for you. I think it is right that he is made aware that his credit may be affected but to also be quite clear that you are not to blame in any way. You cannot protect everybody – you can only protect you and never forget that ‘you’ matter.
Does your mother accept she has a problem? If she does, then self-banning is a terrific way for her to show you (and herself), the sincerity of her desire to live gamble-free.
There is always hope but it does require your mother to accept her addiction. You cannot save her – I am not judging, it is a mistake many of us have made.
Keep posting – you are doing well