Merging 2 video files?

All professional video editing packages support mixing multiple video streams while independently transforming them. See Adobe After Effects or Sony Vegas, for example.

If you need a free solution, you can also use Blender's integrated video editor; however, it is not as intuitive to use as the two mentioned in the last paragraph. It can get the job done just as well, though.

I'll add another vote for Sony Vegas as a decent video editor. It may be overkill for this particular project but you can pick a copy of the basic edition for under £30. (I used Sony Vegas for the exact usage you mentioned)!

For a free piece of software you may be able to get AviSynth to do what you need, though it will be a little more involved than using a graphical editor.

Yea, Vegas is very good for this type of stuff. I used it a long while ago (before it was acquired by Sony) to edit music videos, and it was good enough for pro work even back then. And it wasn't priced so as to break your bank either.

I have only dabbled with the newer versions since I seldom do video stuff anymore, but the diamond-like quality still seems to be there.

I'm not sure what they've done with VirtualDub over the last couple of years (last I know it couldn't do that), but as it's freeware I think you should check it out.

I've used VideoMach in the past with good success.

It's a more lightweight, yet still quite powerful tool for basic video editing tasks.

You could also write a simple C++ application to do this for you (shouldn't take more than a few minutes). Use OpenCV to read and write the videos. It's free and you might learn a little doing it.