Regarding your first question: Is it okay to let your son do things that aren't allowed in Islam (regardless of what you do with other people) the answer is no.
But it is true that Islam itself discriminates, in that some things are allowed for men but not for women.
Another point is, in Islam, kids must obey their parents as long as they don't ask for something contrary to Islam. So Even if Islam does not say anything about going around a tree, jumping three times and clapping your hands, you can still forbid your kid from doing so. If you ask him to steal or to lie, that is different (And I do mean even the smallest of lies, like answering the phone and saying you're not there when you are - My dad used to do that)
That being said, I gather you live in a foreign country, and my comment (which I would've posted as a comment if I could) is this, and is not motivated by Islamic sharia. I spoke about Islam, now I speak of my own accord.
There are two motivations to discipline your children:
Making them better human beings, and making them behave when they are in your presence or under your rule. The former is a noble goal which might bring them closer to God, the latter is a selfish goal of self-satisfaction.
If your objective is the second one, I cannot comment. But I would urge you to consider this: look around you, we live in a different time. I cannot emphasise this enough. All my cousins and my friends who had strict parents either did nasty things when the parents had their backs turned or became the exact opposite of what their parents wanted once they became independent. The façade was certainly soothing for the parents, but it hid very bad behaviours.
I, on the other hands, had a mother who taught me right from wrong, not by imposing them, for when you impose a morality on a child you prevent him from building his own. When I did something bad, she talked, listened, advised, punished but always with my approval ("Do you think this is a fair punishment for what you did?", etc).
I advise you to come to the realization that you will never control every aspect of your children's life. Tell her how it is, tell her the danger of drinking, and such, be there for her if she calls you when something gets wrong (and something will probably go wrong at some points) and you'll make a wonderful human being out of her.