My family was involved in the Irish emigration to Amsterdam, NY at that time period. While they arrived slightly earlier, they were actively recruiting ex-neighbors to emigrate during the peak period you mention.
This was the time that the linen trade was collapsing in Ireland. The Civil War had led to expansion and industrialization of major mills in Ireland. However the "embargo" on cotton trade to England by the North had led Britain to develop imports from Egypt which had much nicer cotton quality. Then, with the end of the war, the cotton trade never resumed with the South to the same extent and the plantations importing linen for clothing slaves was no longer an issue. Neither were linen Army uniforms needed.
Over production in Belfast led to bankruptcy of a large mill and several more perhaps then occurred. The references are a big vague here. However, industrialization was wrecking the draper/home weaver system. Home weavers could not compete, especially if they wove coarser linen. They received linen on beams ready for installing in their looms from drapers and had to give the finished weaving to their draper to sell. However, the growth of the cotton trade now meant the draper was competing with mill woven linen and with cotton goods that were more popular. During that linen boom time, many children had been able to stay in their hometowns as weavers and now needed to find better paying jobs. Emigration was traditional as the Irish generally practiced the rule that only the eldest son inherited the (rented) farm and possessions. You can inspect a few wills on the PRONI wills site to get an idea of conditions.
My folks recruited from the Knocknamuckley area for the carpet industry and the Chiney silk mills in CT recruited from Portadown. Look at the "Old Fulton Postcard " site with its newspapers to discover where the Irish glovers were from. Look at the individuals. Their birthplace would be mentioned in obituaries. I would then look at conditions in their ex-region. This won't be as hard as it seems. Marilyn Cohen and others explored the Tullylish area, but the glovers may not be from there. Tanned leather had been important in Ireland, but I think it died out very early as oak trees disappeared and the British laws stopped the trade. I doubt if the people were glovers in Ireland. If they were weavers originally, I would look at research on the Belfast linen mills. The few glovers I have noticed were women, so where did their husbands work? Did they have husbands as many Irish women had been abandonned or widowed and then had to work in mills. Also look at who were the emigrants who encouraged friends to emigrate? If you go back through Ellis Island, and the directories you can see who stayed with whom when they first arrived. This will help trace folks back to Ireland. I would expect a scattering of emigration locations at first and then a more concentrated region where most people came from.
I found that intermarriage was common among Irish immigrants who had known each other in Ireland and many were active in the Orange order. However, asking about culture is a problem as most of us don't think of ourselves as having a culture. My grandfather was pulled out of high school to go to work and other family members worked at age 14 on. My family was proud of not eating potatoes at every meal. We don't admit to having relatives in Australia as this implies they were were on the losing side, generally considered Catholic, in the 1798 rebellion. Being obviously of the Northern Irish Protestant culture and not the Irish Catholic culture was important in my family. Some folks claimed to be Scottish to avoid being considered Catholic Irish. Religion was very important and mothers had a lot of say in the family determining future occupations and marriage partners, but this may be part of the times and not Irish. Most of the cultural differences disappeared, so you will have to interview people to find what use to exist.
I have a few book on the linen trade in Ireland I can recommend. If you are looking at people are coming from the Amsterdam area, I can help you there but I am not familiar with the glovers.