I know it is easy to say, but try to calm down on alcohol ; not to stop it fully, but being drunk won't help you neither at sex neither in your relationship.
Try to have nice or fun activities with her, even just walking arround in parc, river side, or nice places ; with phones on silent mode and taking the time to be together.
Eventually, confess to her that you feel bad about how you behaved with her and beg her forgiveness ; don't give her too much details, and try not to hurt her while doing so...
You are right, I didn't see she threw a chair at him ; just that she threw a chair.
Also, I don't think all those who have had a bad behavior are needingly bad persones. It seems to have happend once, monthes ago, because of anger. By deduction, it was the worse she has ever done ; and we don't know the context (but Op decided to remain with her after that).
Right or not, Op seems to wish to keep the relationship and to improve it. Maybe you would not if you were in his shoes, and I don't know if I would. I don't know if I would agree with your life choices either. But I agree to respect both yours and Op's own life choices.
And finally, if I someday ask advices to improve my relationship, I would not expect to be suggested to leave, but to be given advices on how to improve it. Else I would be asking advice on "should I maintain this relationship"... So I am sorry you be disappointed that I answer the way I would wish to be answered ; but I encourage you to try to juge less at others.