It is not permissible for the girl's guardians to make her go to this mixed school, because that is heedlessness and a betrayal of the trust. Rather they should prevent her from doing that which is haraam and help to avoid sin, and they should be protective towards her and protect her honour.
It is not permissible for a woman to travel without a mahram, because the Prophet (blessings and peace of Allah be upon him) said: “No woman should travel except with a mahram.” Narrated by al-Bukhaari, 1862.
And Muslim (1339) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “It is not permissible for a woman who believes in Allah and the Last Day to travel the distance of one day's journey except with a mahram.”
As for her staying in a city without a mahram, that is not forbidden if she is safe and remembers that Allah is always watching when she comes and goes, and she avoids mixing with men.
Based on that, if a mahram travels with you and takes you to the city where you are going to study, and you stay there in a safe place and adhere to the Islamic guidelines when going out to the University, there is nothing wrong with that.
If we assume that the mahram cannot travel with you there or back, and your family insist that you study in one of the two choices that you mentioned, and there is no alternative to that, then the basic principle is that you should choose the lesser of two evils so as to ward off the greater of the two. So you have to choose the less evil of the two options. This means that you have to think about and study the two choices. Your travelling may be less evil, because in that case you will avoid mixing, but it involves the problem of your being alone and away from your family in a strange city. If you can get in touch with your paternal uncle through breastfeeding and he can keep an eye on you and help you and so on, then that is better.
You should strive to increase your faith and strengthen your connection with Allah, look for righteous friends and keep yourself busy with good deeds such as memorising Qur'aan, and regularly offering naafil prayers and fasts.
We ask Allah to help and guide you.
And Allah knows best.