Right had a quick search on Google and all I could find for Minato was the G1. So lets try to get this sorted blind
You say you have a 3 way scart switch so:-
Plug VCR DVD & Sky into the 3 inputs
Plug switch box into TV
Connect VCR out scart on Sky to the VCR AV2 input (can then record from Sky).
all obvious so far I think!
Now all the scart cables are putting a signal into the TV, but nothing is coming back out, but I guess you already knew that!

so:-
Your TV is nicam so it should have red & white phono sockets on the back. Connect a set of leads from here to the Minato EC-105B. You now have a signal path back to the amp/speakers and with a bit of luck the kids (and you) are all happy as DVD's are now in DD/DTS

& TV/Sky/VCR are in DPL.
If there are no phono connecters on the back of the TV then you will have them on the Sky box and probably the VCR. If going from the boxes, not the TV, you will need 2 sets of phono leads going back to the amp and 2 inputs on the amp.
Hope this all makes sense.
Mark.