Easiest Way to Split Audio
You don't necessarily need a "splitter IC" (or any form of active splitting). If all the devices you're feeding into have a reasonably high input impedance, then you can just do it with a Y cable: our output can simply fan out to both inputs without being loaded down.  A typical audio splitter will do that anyway, either right at its front door or internally (say, a buffer, which then fans out into more buffers, with the printed circuit equivalent of a Y cable).

When I was teen, I mixed audio with Y cables, and the results were good, luckily. E.g. guitar into stereo backing track, no problem. (But that is generally a silly thing to do because it involves tying together outputs, which could have low impedance, to drive the same input.)


  Re: The trouble is that the signals are combined at the equalizer, so a y cable won't work. I need something to split them without having the signals cross


It is not obvious in your schematic that there are two channels. But if they are simply tied to the same input of the one-channel equalizer IC, then you're doing it wrong. You've basically built a "Y cable" mixer, driving the same input with multiple outputs.

A good way to mix the signals together is to provide completely separate inputs in your system which feed into a mixer circuit. That circuit then feeds your LED machine's equalizer.

A mixer can be made by tying multiple inputs to different resistors which feed the virtual earth point of an inverting amplifier (made using an op-amp, for instance). Good channel separation is maintained because the inputs are tied to the virtual earth node through the resistors, which their currents do not cross. (Channel separation is never perfect: it's just a question of how many decibels. -90 or lower is good).

If you have a virtual earth mixer, you can take the audio out simply by tapping into the inputs.

The audio in circuit in your schematic (which, by the way, neglects to show how two channels of audio are being handled) looks incorrect. You're trying to bring in audio with a single wire, without a return current. This is because your RNG is not connected to the circuit ground. Also, you don't want two resistors there, just one, unless your intent really is to have a voltage divider that knocks 6 decibels off the input signal.

Speaking of which, if you build that aforementioned mixer, you can achieve the decibel reduction by an appropriate ratio of the feedback resistor to the input resistors, to give the mixer less than unity gain.  But for an application like this, it might really make sense to have an AGC (automatic gain control) stage, so that the behavior of the LED box is approximately the same when the volume of the incoming audio changes.