I was able to do:
ORD-LHR (stop overnight, just < 24 hours) on UA
LHR-DUB on EI, stop 2 nights
then DUB-LHR-ORD on EI/UA.
a/i for $581 for April 23-27.
I could not get UA to price it like this so I had to use Hipmunk.
Not quite as cheap as the other fares but a cheap way to get to Dublin and have a stop in London.
Because of the EI codeshare it says it will take 24 hours to ticket.