I'm afraid that this is not really a Remote Buddy specific problem (as 
all Remote Buddy does is open a translucent window - so nothing 
unusual, really), but more of a performance problem of the chipset 
graphics of the MacBook.

OS X graphics system utilizes OpenGL a lot to offload work to the 
graphics hardware. That, however, also means that it'll store as much 
graphics data as possible in the graphics memory, so that rendering is 
as smooth as possible (=> that's also why you'll find 512 MB and more 
on modern graphics cards compared to the 8 MB or 32 MB there used to 
be. Back then, the memory's main use was as a frame buffer, now a lot 
of textures need to be stored there as well).

Now, the higher the resolution you use, the more graphics memory will 
be needed and - especially with chipset graphics (where CPU and GPU 
share the same bus, but can't access concurrently, thus effectively 
slowing down one another) - the more data will need to be shuffled in 
and out of the graphics memory.

When increasing screen resolution and adding a second display, at some 
point you're guaranteed to hit a bottleneck (memory, bus or otherwise) 
and that's when you see performance degrading. It seems your system 
operates close to that bottleneck already and that when you start 
Remote Buddy, the small amount of graphics memory it needs finally 
pushes the integrated graphics of your system beyond its limits and 
the bottleneck is finally hit.

That's also why you'll see zero choppiness with a smaller EyeTV window 
(=> less graphics memory needed, less data shuffled across the bus) 
vs. a full-screen EyeTV window (=> more graphics memory is needed, 
more data is shuffled across the bus).

EyeTV will need more resources than VLC, because it needs to do a lot 
more. While VLC "just" plays back material that's "ready for display" 
right after decompression, EyeTV has to deal with tasks like 
deinterlacing (putting together the half frames it gets from the video 
signal), which means it needs to do some processing on the 
decompressed data prior to being able to display it - which is prone 
to need both more (video) memory and CPU power.

Possible solutions:

- reduce the resolution on your external or internal display (=> keep 
in mind that, unless you receive HDTV, standard PAL/NTSC video has a 
resolution of around 760 x 540)

- turn off any effects you may have configured in Remote Buddy 
Preferences > Menu > Appearance. These all use Core Image and thus 
indirectly put more load (when fading in/out) and possibly more 
resource use on your graphics system

- set a (small) desktop background image consisting of only one color. 
Texture compression on the GPU will make sure the amount of memory 
needed to store that background is minimal vs. a photo as a 
background, which will not nearly compress as much.

- try turning off deinterlacing in EyeTV (may or may not show effect - 
I write that under the assumption that this may save some graphics 
memory and traffic between CPU and the memory on the bus)

Best regards, 
Felix Schwarz