I believe Denis' first wife was Julia Connors.

Denis Mulcahy & Kate McCarthy are listed in the 1901 census. Denis is listed as a Publican and 75 years old (and born in County Limerick). Kate is listed as 52 years old and born in County Cork. Their children are Patrick & Isabella - both 21 years old (they were twins); Kate - 18 years old; Robert - 17 years old; and Maggie - 16 years old. All the children were born in Limerick County.

I have reviewed most of the birth records for the Newcastle Registration District that cover 1864-1880 at the Family History Center. I reviewed the following birth records for the children of Denis & Kate:

James Mulcahy born on March 15, 1879 (Denis' occupation is listed as shopkeeper).

Patrick & Isabella born as twins on April 20, 1880 (Denis' occupation is listed as shopkeeper).

In the 1860s and 1870s I found the following children born to Denis Mulcahy and Julia Connors of Tournafulla:

Cornelius Mulcahy born on February 26, 1866 (Denis' occupation is listed as farmer).

Jeremiah Mulcahy born on October 23, 1867 (Denis' occupation is listed as shopkeeper).

Sarah Mulcahy born on September 10, 1869 (Denis' occupation is listed as Publican).

Mary Mulcahy born on October 14, 1871 (Denis' occupation is listed as Publican).

I have also been recording all the Mulcahy listings in the birth, marriage and death registers from 1864-1958 for the Newcastle, Tralee and Kanturk Registration District after looking at them on microfilm at a local Family History Center.

I found a death listing for a Julia Mulcahy at the age of 42 in the first quarter of 1874 in the Newcastle Registration District (which includes Tournafulla). I suspect this is the death record for Denis' first wife.

I found two marriage records for a Denis Mulcahy after 1874 and before March 1879 (when Denis and Kate's first child was born). The first listing is for the third quarter of 1876 with the marriage occurring in the Newcastle Registration District. The second listing is for the first quarter of 1878 in the Kanturk Registration District (which is in Cork County at the border of Limerick County and covers Rockchapel and Milleen areas). Since the 1901 census indicates Kate MCCarthy was born in Cork County I suspect the second listing reflect your great-grandparents marriage.

Unfortunately the Family History Center only has microfilm copies of death and marriage records from 1864 to 1870 so I haven't reviewed the actual records.

I hope the above helps you get through the brick wall. If you would like to discuss this further, then send me a private message.