Honestly, it can be very difficult for others to get a good idea of what someone with ADHD goes through on a day to day basis. That you felt alone while trying to get the help you needed really sucks because you were on your own fighting that battle at just 13 years old. That really sucks. I don't know the full story, but could it be that your mum relied on the doctor's advice and knowledge and thought they would have more insight in this kind of stuff? I mean, I personally knew I had ADHD before I was diagnosed. When I first went to get diagnosed they said my symptoms weren't bad enough at the time to be diagnosed with it. It was really annoying because I knew I had it. A few years later I went somewhere else (a place where they specialised in it) and finally got diagnosed.
It's quite frustrating but I've had enough experiences that made it clear that I was more knowledgeable about the subject than a doctor or therapist. I even sometimes had to explain how it worked to them. So keeping that in mind, and knowing many people expect a doctor or therapist to be the expert on these subjects, I think it's understandable that even your mother believed the doctor. (My experience taught me that it's never a bad thing to do your own research (like you did) and fight to get the help you need. Sometimes that is the only way to get the help you need. But not everyone knows this).
Now that she knows she was wrong she seems to feel bad that she didn't listen to you all those years ago and wants to make up for it. I understand your frustration, but the fact that she's doing this means she is admitting to her mistakes and wants to be there for you NOW.
They sell it at every supermarket. If you ever visit again you may also want to try Tokkelroom. I prefer it to advocaat. It contains less alcohol and tastes creamier than advocaat (though the general taste is very similar).
To those who are having trouble finding advocaat in their country, it's very easy to make though. And the ingredients should be easy to get in most places. Here's a recipe. :)