Resizing online video

[Maylon_Brando]

Hello,
I've been googling around for a solution to my problem but I was ultimately unable to find one. Here's it is:
I've registered myself on a betting site just to watch live streams I can't watch anywhere else on the internet (had to deposit 10€ but that's still worth it). What I didn't know was, that it's impossible to watch the video fullscreen. It's just a tiny little box which can be enlarged only a bit. I also believe it's a flash video, that's why I posted into this section of the forum. If I'm wrong, feel free to move this thread to the right section of the forum.
So, is it even possible by any means to watch the stream fullscreen or at least at a decent resolution? I've already tried to use smaller desktop resolution to make the video bigger but that actually only made all livestreams stop loading (I mean seriously, how can they know what resolution am I using and that I've changed it?).
I figured out by reading your forum that I might have to record the stream first and then watch it live via VLC player. If it's so, can anyone recommend a software I should use?

Thanks a lot for any help