switters

I need to be in Stockholm on 7/8 and in London on 7/15 next summer for work. Taking my wife and daughter and going to spend some time in Sweden and the UK before/after my work commitment.

I will be using CapitalOne cash rewards to book the tickets, and we'll be flying in J. Just searching for fares, it seems cheaper to fly RT from SFO to STO (I see a fare for $2,600 on SAS, with short layover at CPH), and then book a RT from STO to LHR?

I tried a multi-city fare using Hipmunk but that came out more expensive.

Any tips from those more familiar with flying from the west coast of the U.S. to Europe would be appreciated.