Do  I really have to tell my wife that our daughter is buying alcohol with fake id?
You think it is normal she can buy with fake id?
I'm sorry but no, I don't think that's OK.
It is good to share important facts with your SO. You should try to get help for your child together.
Come on. We can't tell her can we?
It is expected that parents communicate about important matters like children getting into trouble. You should talk to her at a time you think she will be most calm.