While it's obvious that your flight from the US to London is likely on an American carrier, your London-Dublin-London flights are most likely Aer Lingus (flight numbers have an "EI" prefix).
You CAN still break your travel in London, but this should ideally be on your outbound journey.
You should be going over to Dublin just before heading home, because ideally your homebound journey should be commencing in Dublin via London to avoid the onerous UK taxes / APD.
Perhaps others may have more current info as things do change!
Enjoy England, but don't miss the chance for a day or two in Dublin; you'll never regret it!
http://www.dublincity.ie/dublintraff...e16Camera6.jpg