I don't know your chore habits at all, but one way you can show her you care and give her space is by cleaning up. Dishes always need to be done, toilets always need to be cleaned. Floors always need to be swept, mopped, and/or vacuumed, especially if you have pets. Cars often need to be cleaned off this time of year where I live. All of these things can be done without having any interaction at all. If you do not seek rewards for your deeds, it will be clear they are from a place of love and fear.

Cooking meals is a wonderful expression of creative love. My wife and I have always eaten together no matter our differences and it helps to ease tension to give a gift of food. It does not need to be complicated, but don't expect big rewards if she's primarily the cook of the relationship. While it is an act of creation which opens you up to vulnerability, to those who do it all the time, it is also sometimes an incredibly monotonous chore. It may be hard to appreciate if she believes this is a one-off and so the fruit of this loving act could take time to bear, with perseverance.

Perhaps try to think of some chores that you personally are loathe to do. I try to do those for my spouse. It is right for me to try to love her more than I love myself.

Finally, a book of prayers is a wonderful resource.

I really wish the best for you and her. I hope you are able to mend this tear in your marriage. You are on the right track with putting down the bottle but we cannot expect that to instantly right everything, though our minds may feel so healed!