I assume you want to fly at least business class. Depending upon the date you want then the various Ixx fares ex Dublin or ex somewhere EU can work for you if you are reasonably flexible over exact timing and route.

You need to make the booking from DUB to NYC which means you need a 'positioning' flight to Dublin preferably the day before (£ for hotel) or back to back but the later means you have to fly via LHR so the plane you arrive on is hopefully the one you start the journey to NYC on. The later approach carries more risk especially if you choose a (in)direct DUB-(PHL|CLT..)-NYC flight out.

Practically this means flying out to Dublin Thursday to catch a Friday transatlantic returning say Sunday night to get a weekend in New York. The return flight is short (6 hours) so depending upon the plane and service you might not be feeling so good on Monday and still have the wait for the return to LON.

LON-DUB return will cost around £200 for both of you EI/BA or slightly less with non OneWorld carriers - but the protection AA/BA offer across separate but connected bookings can be really valuable.

So whilst the underlying transatlantic flight is cheaper (£800) you have to factor in an overnight in Dublin, which can be real fun and part of the trip, plus the extra time compared to booking direct LHR-NYC. Flying direct DUB-NYC does save you time as you pre clear in Dublin and land at a domestic walk out terminal.

You could both possibly get BA status (Bronze) assuming at least two of the flights are BA. Silver is attainable but not with just a single weekend in NYC.

So if you can stretch to a long weekend, Thursday to Tuesday, you could get a weekend in New York (3pm Friday to 8pm Sunday) plus two nights in Dublin. If you have enough avios redeem RFS CE both ways (leaves you 20TP short of Bronze but it's not worth that much) to Dublin and you will get lounge access from the start to finish of the trip.