Since she didn't know, the real key will be her behavior. If her behavior remains the same, stay with her. If not, the money has made a difference in her feelings.
It's NEVER impossible, but it is hard. Seek professional help from someone who has experience in these type of situations. I've had several similar cases, so I know how hard it is on both people when others are tugging on them.
Things can always be worked out if that is the true goal of both parties. That being said, it requires an extraordinary amount of work and commitment.
Explain your reasons honestly. Just because she drinks more than YOU think, does not make it a fact. It may be that you can't be with someone who drinks more than you should. You'll have to see what unfolds.
It's not that he didn't trust you, it's that he wanted to factually trust you. You should do the same. In this day and age, it never hurts to have as much information as possible in relationships.
Unfortunately, the world has become so polarized, you can no longer make certain comments, even if the intent was innocent. Your comment could, with certain people, be thought of as a gender-related microaggression.
WTF? Is he living in the 1950's? You need to start setting boundaries. Let him do his own laundry, make his own meals, etc. Basically, go on strike with EVERYTHING.
If she can't do it herself, do it together. Don't do it alone. You won't get anywhere.
It doesn't make any difference whether or not you like her. You should not have to pay for his gift. He's old enough to take responsibility but evidently not mature enough. This should be a lesson for him.
He doesn't understand the image he's creating, and does not recognize the potential negative effect it could have on many aspects of his life.