Thank you for all the replies, it's a long post and I appreciate everyone having a read and helping me out. :)
twh: I had traveled an hour and a half for my lesson and was only informed my instructor was not there after I had arrived.
Horsie not leaving the arena was 100% my fault. I have just been working on having a contact when riding, and horsie managed to swing his bum toward the arena exit and was listening to the contact rather than my leg, as that is what would get him out of work faster. At first, I couldn't put two and two together, but after she came to help and said this to me, I was fine. Loose rein, leg on, he came back into the arena no problems. I know it may seem like a simple solution, but it's something that in the heat of the moment I didn't really think about.
My instructor as a really "give 110% every ride" approach and I took that mindset into the arena without having the horsie problem solving skills to back it up. The horse definitely had it over me that day, but I have been able to ride him fairly well and iron out his kinks before, but only with an instructor there.
I have a lesson booked with another riding school today, so if all goes well then my previous instructor can kiss my $60 a week goodbye. :)