Hello Pekka,
Both CueCore1 and CueCore2 can work with a 12 volt power supply. An should use up to 500mA (0.5A).
Both the CueCore and your splitter use 12 volt. So you can run both from the power supply separately.
If your power supply says it can supply 1A you should not connect things which use more power. I do not know how much power is used by your splitter. So I do not know if you can run them both on the same power supply.
If you add the maximum usage of both the CueCore and your splitter together it should stay under 1A.
Best regards,
Guido