Lets make this really simple, if its all one ticket
You check in at IAD
Aer Lingus and United have code share/interlining/eticket agreement
You will next see your bag in EDI
You will clear customs in EDI (use the red or green lane not the blue lane)
You do not need to reclaim your luggage or any other messing in Dublin, follow signs to flight connections, pass through immigration and proceed to the gate. There won't even be a security check. If United cannot issue the onward boarding card in IAD, Aer Lingus will at the transfer desk in Dublin.
This is how the rest of the world operates, the US CBP has its own awkward and unnecessary protocol which only applies in the US, the rest of the world doesn't care and has a much more sensible approach.