I understand your mums opinion on this completely. I mean if you do transition and did 'change your mind' though it's unlikely (I think 2% of trans population), you would be doing that in a school...where people are pretty damn mean. Thing is it depends on how far you want to transition. Do you just want to start dressing that way, or do you do so already, or is this about hormones or binding, or even pronouns and a name change? However if you chose to transition once already in high school, then you run the risk of having other people really notice it rather than if you had started transitioning before then. If you have a school that's LGBT friendly than it shouldn't be as big of a deal but there will still be bigots everywhere.
Also if you don't know why this person changed his mind, than it's hard to determine if he actually felt he got it wrong or that he was to scared to move forward and decided to repress it.
Going stealth in high school can prove to be difficult though, I mean there is the issue of washrooms and gym class as well as informing the teachers before hand and hoping they are accepting. Some schools will not allow female bodied kids to use male washrooms, if there are gender neutral washrooms available then that is a plus. Now I never announced when I snuck into guys washrooms as a kid so nobody could do anything. Nobody knew I went in there.
You know how many kids dad's drink and get a divorces, it's got nothing to do with the trans population. But that sounds like he's having hard time dealing (just from that line) because he feels it's his fault, or that it's not something that's a permanent state of mind that cannot be changed.
Anyways convincing takes time. Perhaps if you have two schools in your area you could ask her if there is a possibility to try transitioning at this school and if things don't work out you can switch. It will give you a good time to explore more of who you are and truthfully decide. I came out once and 'changed my mind' - but not really, I just deeply repressed it only to come out three years later again because high school was a nightmare for me (not trying to scare you though, some people have a really good time in high school).
Wait are you going into high school or another middle school before high school? Kind of confused, sorry. But the same can happen in middle schools, same issues. Kids however seem to be better younger. They grow up and turn into monsters. And then they grow up some more and hopefully grow out of it.
Anyways my best advice is to try and make a compromise with your mum. Talk it over in a mature fashion which is always nice for parents coming from a kid, especially a younger one because it shows seriousness. Discuss everything, the possible outcomes, the extent of the transition and so on. Transitioning early would have been amazing, I wish I could have gone back and done it because everything would have been easier now.
Also here's something you can let her know, I have an endocrinologist (the hormone doctor), and he told me when I went in at the age of 18, that people like me, and even younger knew more about who they were than adults. Because when you are young things are simplistic. You don't have the things to consider that you do when your an adult and have to transition which causes a lot of doubt. Doing it young is a dream a lot of trans people have. Younger people are very sure of themselves, children are not as confused as adults make them out to be, in fact its adults who deal with most confusion. For whatever reason that other kid changed his mind, your mother can not not use that as a basis on her decisions, I mean she can, but she shouldn't. Like I said the kid may have been wrong, but then he may just be repressing everything because of fear, which a lot of people don't see, we have a lot to fear! The transition process can be the most exciting and amazing thing ever, it can bring up confidence and make you happier, but it can also be scary and depressing and leave some pretty ugly scars (metaphorically, hopefully).
Anyways I hope everything goes well. I know I can't help much. This isn't something I was lucky and unlucky enough to go through. Time does wonders, and sometimes the person who can be the most unaccepting can be the most accepting in the future. Some people just fear losing their kid, but that's going to most likely happen whether they like it or not when you hit high school. If it is about losing a kid, then you need to let him know you don't want to lose a parent because he can't accept you, because that can and might happen in later years. I don't speak to my dad (for more than just that reason) and he is no longer a part of my life.
To be accepting does not mean to be encouraging. I know some parents dislike allowing their kid to transition because they think it makes a statement they are a bad parent and are encouraging you to be a boy. Of course that's not true at all, and other people who think that are worth nobodies time.
Anyways, I'm sorry this was so long, tried to help as much as I can. Anyways I really do hope things go okay, I know this can be a very hard time for you at your age, and I ended up doing a lot of things I regretted from repressing like self harming and drinking (though don't ever use that as a threat against parents, just as a possibility of what can happen when you are forced to be something you are not).