When you post, it is important to put enough detail of information for volunteers to fully research the person you seek. Her DOB was GREAT information, but the year of death and the name of her husband wasn't shown. Her father appears to have arrived from Ireland in 1869 with spouse? Catherine Flagerty, the mother of Stephen James Brennan, born 1874. In 1886, he married Mary Keenan in Wisconsin. So, Mary Ellen's mother, Flood, may or may not have been married to him. This and other information is VERY IMPORTANT to research not only Mary Ellen, but her father to see where and when he may have married.
Since you have a posted family tree, post the link to Mary Ellen, as that will give volunteer researchers a good starting point as to what you know and possibly correct some by use of bonifide sources. Almost weekly I find family trees having incorrect information as many just attach wrong information by others or assume the person they have is the same as the person found in records. Genealogy is like a crime scene, you do not want to put the wrong person in your prison.
The link to your tree of Mary Ellen (very nicely done by the way).http://trees.ancestry.com/tree/27868710/person/12594261222
--Posting the link also helps prevent you receiving information on the WRONG people...
The problem... You have attached a lot of information on your family tree which would take a lot of time to verify. There are just to many Michael Brennan that were born in Ireland, immigrated to the US, were naturalized and lived in the US to verify if each birth, immigration, naturalization record and residence were of the same person. Going backward in time from YOUR person's death, posted obit, and burial, would need to be done to "attempt" to identify if this is the correct person as identified. You may have already done such and have documented verification; but a true genealogist would need to take a lot of time to do such...and then not be able to confirm such documentation. A LOT of Great Britain citizens did not arrive at New York, but came through Quebec, Canada. So finding the same named person arriving in Canada and then down to Wisconsin, Illinois and Iowa would be easy to do.
As far as Mary Ellen, a "potential" birth certificate is probably not available to identify the mother. Her father's obit probably does satisfy the fact that "Mrs. Baker" was a child.
Your's is a VERY DIFFICULT process due to SOOOOOO MANY Michael Brennan's.