What is this, and where can I find one today?

I started this thread for an entirely different purpose earlier, but resolved that problem.  Now, since I have a different one, I didn't see the point in starting a whole new thread when I could just edit this one!

So anyway, I've been trying to fix my mom's old Atari 2600 (the only gaming system I had until I got the original PlayStation when I was 11 or so).  I've taken it to a friend of mine, whose dad checked all the internal components, and it's all fine.

The problem seems to lie in the video out.  There's a single RCA-style cable coming out of the 2600, which (apparently) carries both audio and video.  This cable leads to a transformer/splitter of some kind, that I've decided has to be the problem.

Here's what it looks like today:

As you can (kinda) see, the RCA (or whatever it is) cable goes in the top:

and then there are two outputs.  The one on the bottom:

attaches to this little thing that converts it to a standard coaxial output:

But the other output looks like this now (it's attached to the unit):

This part was apparently duct-taped to this little doohickey at one point, as well:

So my assumption is that I just need to get a new one of these

so I can attach that first converter-thing (that outputs to coaxial), and then it should work?

I'm trying to provide as much information as I can because I really don't know what the hell I'm talking about.  I just want to be able to get this old hunk of junk to work again.

So does anyone know what this item is called, and where I can get one today?  I'd greatly appreciate it!