So, the first thing you need to understand is that sole custody isn't just about where you live.
When you talk about custody, you're also talking about the parental obligations dad has to participate jointly in major decisions affecting your care - which school you go to, which town you live in, what your name is, whether you get vaccinated or not. This may not be something you really understand until you have kids of your own 10 or 20 years down the track, but for a parent to forego any say they have in their children's care and welfare is a very big ask. Even the Family Law Act says those obligations can't be removed except by the Court, and it tells the Court not to change those obligations for either parent unless the circumstances are so dire that there really is no other option.
Now, I'm sure you don't want your parents going to Court against each other about this sole custody stuff. It will cost them both a lot of money that they would both probably prefer to spend on you, and because family law is essentially a contest for victory, parents often end up saying terrible things about - and to - each other in order to try and win. It's hard for parents to come back from that, and I imagine you would like for your parents to get along as best they can.
So, rather than look at this as 'I want mum to have sole custody', maybe the happier medium is 'I want to live mostly with mum, and spend some time with dad', which is not at all uncommon for young adults like yourself. I'm sure dad will probably be a lot more welcoming of your wishes if he knew you didn't just want him ousted as your parent, that you still wanted to spend time with him, too, even if it was just every second weekend and maybe a dinner during the week.
But the question is, what's the best way to make that happen with as little conflict as possible?
My suggestion is to talk to your mum and dad about attending a child-inclusive family dispute resolution conference.
A child-inclusive family dispute resolution conference is where you will get the chance to speak to someone without bias about your situation. They'll hear your views about what you want for yourself and why you want that, and then they'll convey your thoughts to your parents so they can take them into consideration when discussing possible changes to your care arrangements.
If things don't work out and your mum and dad can't agree, then they can file for parenting orders through the Court (though hopefully, this will be a very last resort - Court really isn't fun for anyone). If that happens, the Court will take your views (among other things) into consideration when it's determining what's in your best interests. Being 14, your views would probably be given a lot of weight by the Court, but there are lots of other things it has to take into consideration, too.
Anyway, I hope I've given you some things to consider. If you have any more question, please feel free to ask.
