Ok so while there are a lot of 'I think' posts in this thread, there's not a lot of 'try this.'
So. Firstly you should call uni/your halls and ask whether guests are allowed to stay for a night. If it's a no, then you have your answer. 'Sorry mum, I tried...'
If it's a yes, have a mature chat with her about how you feel. This is your first night to bond with flatmates and get a feel for uni life. As much as you love her, you don't think it's appropriate to stay together on your first night and your flatmates more than likely wont appreciate it either. Tell her you appreciate everything she's doing to help and you understand asking to get a hotel is inconvenient for her, but you would really appreciate if she took up your offer of staying elsewhere. Suggest you meet for brunch before she leaves so you can say proper goodbyes and wish her a safe journey.
If she's still insistent you'll need to be a bit firmer. 'No mum, this is a big event for me and I want to do this on my own. I know you want to stay together but I feel that it could really impact my first few days settling in to uni life. It's like going to your first day at school and having your mum sit next to you at your desk.'
Hopefully being honest about how you feel (don't say you'll be embarrassed or you'll be made fun of) she'll realise what this means to you. If not, well, then it's incredibly selfish of her and you'll have to decide whether to let her 'win' or have a fall out. It might mean you travelling up on your own though...