Using an audio splitter when using Arduino to read from an aux cable
From what you've described I can think of two possible issues:

1) If the audio splitter stops the Arduino from reading values even when the speakers are not connected to the splitter, then you have a dodgy splitter (simple enough).

Try verifying your splitter by checking the resistance between pins at either end, including your additional cable. If there is an open circuit this will be very apparent.

2) If the drop-out only occurs when you add the speakers, you are loading the headphone output of your laptop and that is dropping the voltage to beneath what you can measure.

From a quick bit of googling I found that some basic PC speakers have an input impedance of around 10 kΩ. Presuming you are using the analogue input pins on the Uno, they have a very high input impedance of around 100 MΩ. 

Given these numbers I would actually find excessive loading to be a bit surprising as headphone outputs are intended to drive much lower impedances, down to around 32 Ω.

Do check out your splitter and report back!