I can understand and sympathise with your parents' position even though I totally disagree with it. This is your life. Your future. You have to make the decision that is best for you, based on your needs and what you want from a university. Your parents are just worried about you I imagine but even so they're out of line to try and control where you go.
I recently firmed Lancaster and went an open day in September and absolutely loved it! I obviously couldn't give you a student's perspective on the uni (whereas I'm sure many people on TSR can) but I can tell you a little bit about some of the various perks and things they have there general to the university that you might not find on the internet.
Also, have you considered ordering a prospectus? If not, I highly recommend it. It has a lot of useful information in which is easier to navigate than a webpage. Also look for student vlogs on YouTube... they can give an interesting insight into student life sometimes as well
I nearly applied for Loughborough but didn't. I'm the opposite to you. Loughborough is a 3 hour train ride away for me and Lancaster 40 minutes by car. For you, maybe coach travel could be a cheaper option? I've never used it in my life but my mum recently used it to travel to Nottingham to visit my sister and it was cheaper than a train fare.
But, bottom line, if you want to go Lancaster, go Lancaster, and I would encourage slowly and gently trying to bring your parents round to the idea of attending an applicant day, rather than just getting angry with them and having a forceful conversation. Show that this means a lot to you and in the end I don't think they would try and deny you going to Lancaster if that's what you really want
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