Starting with what we know
Mary Collins from Kilthomas married Thomas Casey from Kilbeacanty.
They had four children that we know of.
Ann ,Mary, Thomas and John (1834 -1912)
John is your great parent and went to Indiana.John married Theresa Sennett (1850-1917) in 1868. Presume in the USA .he arrived in the us in 1861 aged twenty seven.
So far I have not found anything on Mary who married a keough and had a son Patrick who did not marry.
Thomas had two to five kids that went to Boston and unknown spouse
Where did you get the information on Mary and also on the numbers of children mary and Ann had and how many went to the states
I am still investigating Mary and Thomas but nothing definite as of yet.
Regarding Ann .you say she married Mullins had several daughters all went to the USA .
I have found online baptism/birth certs for six children parents Ann casey and Michael Mullins.these are in Kilbeacanty the town land of Drummin. There were five girls and one boy.My source is Rootsireland.ie a pay site.
They were
Mary DOB 18/August 1863
Winifred DOB 08/July 1865
Bridget DOB 19/August 1867
Thomas DOB25/December 1869
Anne DOB 09/March 1873
Margaret DOB 18/March 1878
I notice that the sponsors were mainly from the local town land as well.
I have the details from Drummin under town lands here
http://www.irelandxo.com/group/kilbeacanty-galway/townlands/drummin-druimin
In the census of 1901 there is Ann Mullins(nee casey) the mother now a widow , Thomas and the youngest girl Margaret.
In the census of 1911 Margaret has left.
http://www.census.nationalarchives.ie/pages/1911/Galway/Kilbeacanty/Drummin/903062/
You will note that Ann was Irish speaking.(Look at the PDF of the original)
Looking at the census you can see that there are two Mullins families as well as well as two Caseys.
Last week the Caseys produced a book about their family and ancestors.I hope to get two copies of it and I will get one to you.
http://www.galwaynews.ie/31391-casey-clan-gathers-launch-family-history
I have not as yet been able to identify a link from your Casey to them but I have concentrated on the Mullins link at the moment.i hope to clarify what I have found on the Caseys soon.
Looking a little further back
Griffiths valuation of 1856 identifies three Caseys in Drummin Margaret Michael and Thomas,as well as a John Casey in kilcrimple. Again you can see this under townlands
Remember the griffiths is not a census it only lists the heads of taxable (enough land)households.
There are no Mullins mentioned in Griffiths.
Neither Mullins or Casey are mentioned in the applotment book of 1827.
Regarding the Collins in Kilthomas
I see three mentioned
Michael in drummina-coosaun
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&PlaceID=543871&county=Galway&barony=Loughrea&parish=Kilthomas&townland=%3Cb%3EDrumminacoosaun%3C/b%3E
Margaret in Knockoura
Mary in Knockoura
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&PlaceID=543926&county=Galway&barony=Loughrea&parish=Kilthomas&townland=%3Cb%3EKnockoura%3C/b%3E
You can see that one of their neighbours is a Sinnott.the only Sinnott in Griffiths for Galway.There are only a few Sinnotts in the Galway census of 1901/1911.they were born in India.
Could these be the family ofTheresa Sennett ?