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Could you help me with some additional detail.
Do you have a sky or DVR box you want to be able to watch in another room, or are you wanting to stream whats on your TV eg Netflix to another TV?
If I understand you correctly you want to mirror whats shown on your main smart TV, on another TV in the kitchen, so you can watch Netflix for example.
I dont think this will be possible as most residential TV's do not have a video output, which is required to mirror the display, clearly you can use your Sky Q Mini to tune into the same channel, but that wouldnt give you the ability to just switch the TV on in the kitchen and continue watching whats shown on the main TV.
However to double check, can you give me the model number of your main smart TV.
The digital optical out is for audio out to something like a sound bar, or home theatre system.
On checking further into the specs I can confirm there is no video outputs, and there are no apps available to stream your content to another device.
At best you could take the HDMI feed from your Sky Q box which goes to the Main TV, split it, and then install a cable between the Main TV and the Kitchen TV so what ever you have on the Sky Q box is visible on the Kitchen TV, but that wouldnt give you the ability to watch content you have on your Main TV such as Netflix on your Kitchen TV.
Please let me know if I can provide any further assistance or if you need anything clarified.