When you swore your marriage covenant with your husband and God you were well aware that he came from a fundamentalist background and he was opposed to you drinking, this discussion honestly should end it there. You need to honor that even if it's a little heavy.
If being married to a fundamentalist who doesn't want to be around alcohol wasn't what you wanted in life the time to address that was BEFORE you got married.
This is not advice that will create a relationship where both parties are strongly in love with each other.
Actions in a marriage that are taken against one or the other's desires cause a loss of love units in the person who is being coerced. It's just a fact.
An agreement in a marriage is valid only so long as both parties are enthusiastic about it. If circumstances or experiences cause the other party to lose enthusiasm about the decision, the couple needs to renegotiate it until a new solution is found they are both enthusiastic about.
That is very much his right and if that is his conviction he is 100% right and Godly and consistent with scripture.
This is not a sentiment that will create a happy marriage. Not sure what the foundation for this comment is, but the wife has her own spiritual free agency, conscience and relationship with Christ. He doesn't have some Godly 100% right to force his convictions on her, and doing so would NOT be consistent with Scripture.
you being his wife need to respect his beliefs, they are indeed biblical.
Much, much harm has been perpetrated on people because one person declares something "Biblical". Abused wives are further buffeted by and suffer from such advice because anything that is hard and is wrapped in the cloak of "Biblical" can be made to feel like it is your Biblical duty when in fact is it anything but! Marital suffering is NOT a Biblical duty; marital suffering is not meritorious. Marital JOY is what God hopes for a marriage.
After dedicating so many years to suffering under "Biblical" this or that, I came to realize that whenever a person throws "Biblical" at me, it's just their interpretation - it is not actually the Bible's interpretation. I no longer accept anyone's edicts of something being "Biblical" without researching it with skepticism. If it passes a skeptic's test, then I will consider it.
In this case, your suggestion that a wife deserves to continue suffering under her husband's edicts is far from Biblical. His behaviors influence her desire to keep her bargain. He is exhibiting poor marital behaviors which are influencing her willingness to continue on in the bargain.
Lying about drinking is indeed honestly one of the primary signs of an alcoholic, it doesn't sound like you are but it should be said.
Onerous and punishing behavior on the part of a spouse that tempts the other spouse to lie rather than face the consequences is one of the primary signs of martial relationship that is crying out for help. In this case, if the OP's narrative is all true, there is no indication for AA. It seems like a tactic of her husband's to shame and punish her for not wanting to comply with his demands. It escalates his consequences to emotionall battery so she will just comply better with demands she doesn't want to in the future.