Do you have Bridget's dc? and if so, what info is on that?
The info on a death registration is sometimes far less reliable than first hand information, so you need to consider who was the informant, how would they have known the info, and many other factors, including that they were likely suffering grief.
Please don't spend your pennies on the NSW BDM real deal certificates, please, if you are ordering certificates, please consider the alternative option which NSW BDM promotes on their own website. (Cheaper, already transcribed, comes as email attachment

)
http://www.bdm.nsw.gov.au/bdm_fh.html#transcriptionAlso do remember that sometimes the Dads registered their babies, and so the info that Dad gives about himself should be more reliable than his 'second hand' info about his wife. And of course, sometimes the Mums register their babies, and so the info about herself should be more reliable than her 'second hand' info about her husband.
If this were my family, I would hasten slowly, and obtain just the one document to start, .... so I would consider a full transcription of the birth registration of the youngest child. But, if you do not yet have the birth registration for your own direct line, then perhaps you may want to obtain that official transcription too. And perhaps you would be striking it a tad lucky and find that Dad registered one and Mum registered the other .... and so compare their memories too
Cheers, JM