Hi Bambi
Thanks for the update. As Sinann says you don't need to sign up to familysearch.org. It's a great website as it allows you to search for free the indexes for births, deaths and marriages for Ireland and gives the reference numbers/details you will need if you want to request the certs from the GRO. One of the problems with the birth indexes is that they only started recording the mothers maiden name in 1928 so the search for births of surname Curry with mother = Dunne will only return the ones after 1928 as in Sinann's last link (George, Ellen and Thomas). You could request one of these certs to see if the details corresponds with your family and gives you any more useful information.
I would also recommend ordering the cert for Kevin Curry born Q4 1920, Dublin South, v2 p619 as this is the most likely candidate for your uncle. I also think (but cannot guarantee) that the record of Mary Christina Curry born Q1, 1927, Dublin South, v2 p387 is very possibly your mother so I would also recommend obtaining this cert. Bear in mind that Q1 1927 means that the childs birth was registered sometime in Jan - Mar 1927 and so could have been born in December 1926 (which would tie in with your mothers birth month - perhaps she just got the year wrong?).
I also think that, as Sinann said previously, Celbridge and Leixlip are just over the Dublin border into County Kildare and so there is a chance that your grandparents were living there and your Grandmother travelled to a Dublin Hospital to have her children. Holles Street Maternity Hospital is on the southside of Dublin which would tie in with the registration district. And as your mother's address on the marriage cert was Leixlip there is definitely a link to this area. And so I also think the marriage of Michael Curry and Mary Dunne registered in Celbridge, Q2, 1921, v2 p404 is most likely your grandparents.
Well, it's mostly guess work at this stage, not sure what you'll think of it, but if I were you I'd get 3 certificates:
Marriage of Michael Curry and Mary Dunne, 1921
Birth of Kevin Curry, 1920
Birth of Mary Christina Curry, 1925
Let me know what you think and if you need any more information. (Sinann your opinion would be welcome to!)
All the best
LostandFound