Hotel Booking - Rights

Hello,

next week I'm going to Scotland for the Open Championship. The trip was organized in February and I booked a single room in a two-star hotel for the price of an average UC return flight via bookdirectrooms.com xx(
Now, recently I cancelled my Ryanair flight to Edinburgh and book Lufthansa to Manchester via Munich for less, but this means that including train ride I'll only be arriving around 11 pm.
The issue I have with my booking is the following: I found the available room online and called the hotel because I had some questions regarding transportation. A rather rude lady told me that they were fully booked for the week and completely disregarded that I had found availability. So I went ahead and booked the room online ):
Since then, I've sent them mails and also called them several times to confirm the booking and the late check-in, but I never got an answer and the receptionist hung up after I had quoted the booking reference. I'm sick of trying to contact them, so my question is whether I should just show up and risk not getting a room, and especially how I should react and what I should demand in case I'm sent away. I've got a confirmed reservation and a partial payment has been charged to my credit card. Needless to say that all the hotels closer to St Andrews than Edinburgh are fully booked. Thank you in advance for your help

The company you booked through (despite the name) will either have an allocation of rooms themselves or have bought from somebody else's allocation.
They will not give the hotel your name until a week, or even 3 days before you arrive so the hotel will not have any idea what you are talking about until they get this name list from whoever holds the allocation.

The best thing I would say to do is to take all of your confirmations from your supplier but also the day before call up to advise them that you will be checking in late. This way they will know you are going to be late and will hold your room and you can know that they have got your details.

The problem with booking through an intermediary is that your contract is with them, not the hotel and you can't confirm anything until just before you are due to check in.