Need advice on my brick wall - great grandmother from Clare

Hello, I am new to this site but was hoping for advice from all of you.  I've been researching my ancestry since 2011 and have had decent luck with most of my great grandparents, all of whom have Irish ancestry.  However I seem to be quite stuck on my great grandmother Margaret Mary Lynch who ironically I knew a bit more about headed into my search than any other ancestor.  
 
According to her 1943 death certificate Margaret was born November 21, 1863 in County Clare to Martin Lynch and Ellen McMahon.  She had at least one known sibling Ellen, known as Nellie, born in December 1870.  Margaret told her family she was from Ennistymon but I can find no evidence of her birth (which I realize predates civil registry but I've searched baptismal records), Ellen's birth, her parents' marriage, or her father on Griffith's Valuation in Ennistymon or elsewhere in Clare for that matter.  I've search on Ancestry, in the civil registration, baptismal records on Ancestry and  Rootsireland, and the Clare Library sources.  Oddly I have found nothing for any member of the family so I am beginning to doubt all or at least parts of the facts I am dealing with.  
 
Margaret immigrated to the United States in early 1880's, settled in Hartford, Connecticut and married James Flanagan there in 1886.  Her sister Nellie followed her to Hartford and lived there until her death in 1938.  Margaret had 9 children: Thomas 1887, Helen my grandmother 1888, Peter 1889, Mary 1891, Margaret 1894, Agnes 1896, Ann 1897, James 1899, and Alice 1902. I have thoroughly traced all her children and grew up knowing many of these 2nd cousins.  Her sister Nellie never married and has no descendants.  
 
I have taken both the Ancestry and 23 & Me DNA tests and on Ancestry have identified a few 3rd and 4th+ cousin matches on this Lynch line.  Interestingly a number of these matches have the surname Carey in their trees and come from the Kilrush area, namely Carnacalla which may now be known as Carrowncalla.  I have built out trees for some of these matches and have had success finding documentation for them further making me think my data on Margaret is somehow incorrect to some degree as I have literally never found a thing for her family.  My hope was the dna match trees giving me insight, but I think the answers are hidden in being able to push Margaret's information back further to find the common ancestor.  Perhaps Margaret's family was from the Kilrush area originally but moved to Ennistymon in her lifetime?  This is why I expanded my search beyond Ennistymon and focus at least on dna matches as hints. 
 
Any guidance or advice would be greatly appreciated!  Thank you in advance! 
 
Kate Lipka