The site indexes are due to be updated with additional information. The information I gave you came from the GRO. I will give you a scanned copy of the extract in the coming week All source information will eventually scanned and posted against each individual record.
At this point my guess( which I shouldnt do) is that Winefreds Parents were John Glennon and Mary Mc Dermott. The Death Certs hopefully will confirm this and we can take the research further.
You can obtain a birth/marriage/death certificate from the GRO http://www.groireland.ie
For research purposes the same information(and less costly) can be obtained by ordering from the GRO a copy of the birth/marriage/death entry in the Register. About 4Euro an entry
The two births which may be of interest to you are as undernoted. I do not have info on these but you will find a little on the second record on http://www.Familysearch.org
I have set out the references as you may wish to order same from the GRO
Winefred Glinnane District Portumna Volume 9 Page 504 Year of Book 1869
Winifred Glinnane District Loughrea Volume 19 Page 420 Year of Book 1866