Hello Kellie,
yes I think it looks very likely from the census evidence that Thomas, Sarah and Bridget are siblings and have a mother Sarah.
We know that Thomas gives Mayo as county of birth.
Belfast has been given at one time for both Sarahs but that was dittoed and therefore, could be very wrong.
Rowlf, has seen evidence in parish records about the family (including Roscommon
for Sarah's birthplace) and it would be good to check witnesses/ addresses and godparents from those records to see if that helps.
The difficulty with Mayo records is not so much that they are destroyed- many do exist but you need a townland and parish.
Griffiths Valuation which is dated around 1850s
http://www.askaboutireland.ie/griffith-valuation/index.xmlhas several Patrick Golden and variations.
I hope that you and rowlf have a bit more info now from Burnley and that perhaps rowlf may be able to fill in a few more details from those parish records.
heywood
