There are numerous variations on this type of naming pattern - it was not always followed exactly. Families varied in their propensity to re-use names of dead children - some did so repeatedly (up to three times in two instances in my families), others did not (more numerous instances in my families).

There are two places named Rhymney in south east Wales: there is the ancient parish of Rhymney, Monmouthshire on the coast immediately east of Cardiff, and there is the large industrial town of Rhymney that spanned the border between north east Glamorgan and north west Monmouthshire and had its church in Monmouthshire. This industrial town spanned the ancient parishes of Gelli Gaer in Glamorgan, and Bedwellty in Monmouthshire. A separate new parish was formed around the early 1840s in the town of Rhymney, with the new church being situated on the Monmouthshire side of the border.

Llangattock-juxta-Caerleon is situated at Caerleon, a little north of Newport in Monmouthshire.

Morgan is a commonplace surname in Wales and borne by around 5% of the population in the areas mentioned above in the nineteenth century. There is a strong chance that the two baptisms and deaths pertain to unrelated families.

The parish registers are in Gwent Archives and in Glamorgan Archives; the Bishop's Transcripts are in the National Library of Wales. The relevant county family history societies have transcribed many parish registers and offer them on fiche and on CD. Extensive portions of these counties' registers have been transcribed by freereg.org. It's worth checking both to see what is available on line and on CD or fiche. Many county archives will undertake small pieces of research for very reasonable fees, or can recommend independent commercial researchers.

Good luck with your research!