The BA LGW-DUB service is an ATR, and is usually 2 flights a day, but one a day at weekends. Aer Lingus is stopping its LGW service shortly.
There is BA834 from LHR on Sunday 4 August, departing 10:35 hrs, so did you get the right date? Or some other unmentioned factor?
Being Emerald you can guest one person, assuming your child is over 2 years old, so either you will need to travel Club or ditch one member of your family. There's no guesting on Aer Lingus, it's just for the BA Gold cardholder. Wetherspoon in T5 is open to all, but probably Pilots or Gordon Ramsay would be a better quality experience.
The Conrad in DUB is a good hotel but not perhaps as good as some other Conrads.