I've had a good friend had this happen to him, similar story, she loved him, thought the world of him but it ended in tears again. He was totally under her thumb after the first time her forgave her, so just take this into consideration what im about to say.
If you do stay with her, this is seriously going to be on your mind for the rest of the relationship. Every time she goes out with her friends, your going to be at home watching saturday night tv, going out of your MIND thinking of what she's doing. It will be the ONLY thing on your mind. It will EAT you up inside making you SICK for that feeling that it's happening again, and you know it. It's impossible to trust her again, no matter HOW drunk or HOW much she regrets it. Alchohol DOES bring out people's true personalities and feelings.
The table's will turn too. She won't trust you and she'll go on a para trip when your out with your mates. She will question your night out, even accusing/hinting of you cheating. She might even follow you and stalk you! She will go through your phone, and emails when your on the toilet taking a dump. She will hate you talking to other women when she's around, and the relationship will break down eventually costing you the ball ache of a divorce and money making you think "why did i not just dump her when i had the chance".
I do believe some people deserve a second chance, but not when they break your heart they don't. Another thing, why should you have to prove anything to her anyway? Did she ask you to marry her?, just so she gets that little bit of proof that you love her when you said yes?
I guess i just don't believe in marriage. It just seem like an old fashioned excuse to prove to someone that you love them and vice versa. Complete waste of time. If anything, unmarried couples who have been together for years and years have already proved their love. They know they love each other, so what difference is marriage going to make?
Also why didn't you stop her there and then? I might sound harsh here, but i think you need to grow some balls, be a man, stop crying to a load of strangers and tell her to F off!