Mate, firstly alcohol isn't the solution to this, if you're going into these conversations drunk, you're going to say things you will only regret later.
This is a very difficult situation. You should NEVER have to think twice about doing something for your daughter. And you should NEVER have to justify doing something nice for your daughter. As others have said, this is a very important thing in your life and an issue you cannot leave to fester, it has to be sorted out now one way or the other. If you're going to spend the rest of your life with this woman, there cannot be tension on this issue. It will only get worse.
However, this has been your partner for a while now. It isn't a fling you can just discard. There is clearly something very important for you there too if you've been together this long and are planning your wedding. You need to sit down and have a (sober) conversation with her, explain to her that she is very important but that your daughter is as well and that you should be able to do nice things for your daughter without feeling guilty or having trouble with her afterwards. You shouldn't have to feel like yolul have to sneak around/ feel guilty for trying to be nice for your daughter, especially when I'm guessing she doesn't live with you.
This thread is making me incredibly glad my wife doesn't care for V day etc