Cindy,
The church records for Mullavilly only start in 1845 so getting back earlier than that will probably be very difficult, if not impossible. So I see no easy way of finding out Peter & Isabella’s parents names from Irish records, but you might be able to find them from US sources eg a death certificate.
To have married in that church indicated that at least one party was resident in that parish. (That was a general church requirement). Tradition was to marry in the bride’s church, so it’s most likely the Curtis family were from that parish. The groom might be from that parish too or he might be from an adjacent parish. He probably didn’t live very far away. Before the bicycle arrived in rural Ireland (around the 1860s) most courting was done on foot, so that limited your scope a bit. Consequently you tended to marry someone who lived nearby. Often the girl next door. So Peter probably lived in Mullavilly too but that’s not certain. And as a labourer he may have moved about a bit to follow the available work.
Since we don’t know anything about Peter & Isabella other than that they lived in this area in 1846, and left shortly afterwards, then it’s hard to know where to look. There are unlikely to be any other records of them in Ireland apart from that marriage record. The church will have no other records other than those on Ancestry and the nli websites. Sadly RC marriage records from that period were very simple. Little additional information apart from the date, the couples names and their 2 witnesses.
You mention the spelling of the surname. The idea of a single or correct spelling for a surname (or a place name) is very much a recent phenomenon designed to meet the needs of modern officialdom. Before that, especially in Ireland, there was no consistency. Names were spelled phonetically and each variation was down to the whim of the particular person recording the information. You will often see the spelling change as the records go back. This rarely indicates a deliberate decision to alter the name, nor even a mistake. Not everyone was literate, but even when they were, exact spelling simply wasn’t something they bothered about. In addition to varying the actual spelling, O’ or Mac prefixes were optional and were often omitted.
In Irish (gaelic) the spelling and prefixes vary depending firstly on what case is used (eg genitive usually requires the insertion of an extra “i”), and secondly with a woman’s name, it changed according to her marital status. It is a further factor in explaining why no-one in Ireland worried about the “correct” spelling. There wasn’t one.
Here’s an example of spelling varying within the same family in the same census:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Sharvogues/Drumsough/920148/
Expect the spelling to vary. It was the norm.
Regarding Peter’s occupation in Ireland, Mullavilly was (and still is) a rural agricultural area. That he was a laborer in the US tends to indicate he didn’t have a trade eg stonemason, shoemaker, carpenter etc because if he did you would expect him to have pursued that in the US. Those sorts of skills were in demand and better paid than labouring. Therefore he was probably a labourer and weaver in Ireland. That’s what the majority of the population were in this part of Ireland. It was also one of several factors that encouraged them to migrate. Due to increasing mechanisation, the demand for labourers was starting to fall, and work was therefore slightly harder to find. (Whereas someone with a trade might find a bit more local employment). There were other important factors behind the mass emigration but you tend to find labourers migrating more than farmers due to their weaker economic position.