^ Parents are smart enough to know what's up if someone's saying that kind of stuff. My best advice is either hold off on that kind of content or do it without any vlogging/video of her in it. If she wants to talk about it over mic, and has some other video in the background (her playing games, or some slides about what she's talking about, or some pictures or other video that doesn't feature her) then at worst someone could find it and say that sounds like her, and she could just say it isn't.
Also advertising breaking the law online is a really bad idea, especially somewhere like YouTube where it's fairly easy to find out who you are if you aren't using a lot of precautions - this is doubly true if she's younger and still living with her parents. While talking about taking drugs isn't a crime, it can be used as grounds to get a search warrant, and if the house she lived in was busted into and drugs were found, the parents would be the ones going to jail not her, so it really isn't fair on them to take that kind of risk even if it's highly unlikely.
If the videos are just to share with a few individuals that she perhaps smokes with or whatever, then make the videos private and just share them with the people in question. If she wants to vlog about it publicly then really she wants to be living on her own - at which point she shouldn't be too concerned if her parents find it, because she's old enough to make her own choices and living in her own place so the consequences don't fall back on them.
Most parents wouldn't want you to drink, smoke cigs, smoke weed, or any of that - but if you're an adult, living on your own, being responsible, and paying for it out of your own money, they might not be pleased but they're probably not going to be as upset/angry as you'd think. If on the other hand you're not an adult yet, living with them, using their money to pay for it etc - then for obvious reasons they wouldn't be happy, and you're putting all the risk on them so they certainly have the right to be.
Just my 2c
Edit: I wrote her because I saw you put she at one point, but elsewhere you said he, so just substitute the she's for he's if it's a guy
Also as far as general channel privacy goes. Use a channel name rather than just using your real name as the name of your channel, keep any especially private videos private or unlisted and share them in the appropriate manner with only the people you want to see them, don't connect the name you use to your real name in any way.. If someone finds it and sees your face etc they're going to know its you, but the chances of that aren't all that high until you hit a very high subscriber count - unless the person in question is looking for the kind of videos you post to begin with, in which case if his mum is looking for videos about people toking up, she's probably not as against it as he thought.