Hi,
I have noticed from the 1861 census that Richard's elder brother Hugh is also with the family in Liverpool.
Looking for his birth/baptism in Llanbadrig around 1814 led me to look at Familysearch.org and this suggests that the birth place could be Llanfflewyn -
Hugh - christened 5 June 1814 at Llanfflewyn
Richard - christened 24 November 1816 at Llanfflewyn
Owen - christened 5 Sept 1819 at Llanbadrig
All three show the parents as David and Ann and their address for Owen's christening was Ty Newydd Carregcefn which is about 3 miles from Llanfflewyn.
I know it isn't easy getting the right family connection with the names being so common but offer this as food for thought. Just to make it more difficult there is a christening for a Hugh Hughes in Llanbadrig in Oct 1815 but this doesn't quite fit with the 1861 census which shows his age as 47 (hence the leaning towards the 1814 christening in Llanfflewyn)
Alan