Well blue I am surprised you have never had any eggnog... it actually is very much like your advocaat. Here is a recipe for homemade eggnog, but honestly I buy it in the dairy section of the supermarket in a carton and then add my own rum...
12 jumbo egg yolks
1 pound granulated sugar
1 quart whole milk
1 quart heavy cream, lightly whipped
1 liter spiced rum
1 teaspoon vanilla extract
1.Beat yolks in a large mixing bowl. Gradually add sugar. Beat until mixture thickens. Stir in milk and rum. Pour into a large punch bowl and chill for 3-4 hours.
2.Fold in whip cream before serving. Garnish with freshly ground nutmeg.
There are variations of course and some use brandy or other alcohol... some even make a cooked version. I am going to have to go to the store talking about this.... I want some about now!
I was thinking yours would be fizzy with the lemonade in it, but the way you describe it, it sounds like a mad scientist
drink and lots of fun.... wonder if it would work with eggnog in a similar manner?