I'm inclined to agree with Mark.Yudkin. I believe the Switch Box he selected is a 3-into-1. Actually the box is completely passive so it works in either direction - 1-into-3 or 3-into-1.
That would allow you to have independent inputs for each device. One for the Turntable, one for PC to Speakers, and another for PC to Headphone Amp. The only drawback is you can have two devices on at the same time. Though that is not much of a drawback.
You can connect one Output to several Inputs, but you can not connect several Outputs to a single input. When you do that you are tying the output of more than one amp together and that risks shorting them to each other.
In your case, from the diagram, you have the output of the PC tied to the Output of the Phono Pre-Amp. I can't guarantee that is a problem, but very likely it will be.
Though perhaps I'm over-simplifing this in my mind.
You have PC to Speakers, and PC to Headphone Amp. But you have Turntable (pre-amp) to Speakers. So, you don't have a common source or a common destination.
I would suggest you Split the PC output with one leg going to the Headphone Amp, and the other leg going to a switch box. The Switch Box will allow you to switch the speakers between the PC and the Turntable as the source. The Headphone amp will be controlled independently. If you don't need Headphones, simply turn the headphone amp down or off.
Steve/bluewizard