Is it permissible for a married woman studying at a public university to demand from her parents to enter a private university or to receive the equivalent amount of its costs for travel, following the example of her sister?

Your father is not obligated to enroll you in the same university as your sister, nor to give you the same amount of money he spends on her education, given her need for it and your lack thereof. The prohibited favoritism among children is that which is pure favoritism. However, favoritism that has a reason, such as one child needing marriage while another does not, is not prohibited.