ICOCA card Haruka Line..etc

Hello,

I'm really confused on which card to buy.. JR card or this ICOCA/Haruka card.

My itinerary as follows:

• Kansai airport --> Kyoto (one day trip) --> Osaka (tennoji) --> Kansai airport

In Kyoto, I would like to visit Arashiyama and perhaps just around the central town.
In Osaka, I will go to Kyocera Dome, Universal Studio and just around central town as well..

It says that the ICOCA/Haruka card is for round trip from Kansai airport to Kyoto/Osaka and back to Kansai airport again.
But if i go from Kansai airport to Kyoto and come down to Osaka before going back to Kansai airport, does that consider as one round trip? Or should I buy another ticket in Osaka when I want to go to the airport?