You should convince your mother of the advantages of the first school.
Which parent wouldn't want their child to go to the best school in the country? I mean, your mother is right that commuting not just be very annoying but can also get tiring after a while. But if you are willing to follow through with it, it shouldn't be a problem, I think. In the end it will be you who has to travel up 2 hours each day. If telling that to your mother doesn't convince her, you should tell her that once you start working somewhere, you most likely won't be able to choose the work place closest to your home either.
In the end, it is you who has to be happy with your decision.