Heffernan help/New York Catholic Protectory

Hello,

I am a new member and kind of a newbie. I am trying to find information for my Heffernan ancestors.

My great-grandfather is Lawrence Heffernan DOB: Sept 1, 1906. I found him in the 1940 and 1930 US Census with his wife Anna and child(ren) Lawrence Jr, Rose (my grandmother), Catherine, and Anna May. He listed his parent's names as John Heffernan & Margaret Dignan on his marriage certificate (#31717) in 1927. I believe his father is sometimes listed as John and sometimes as Joseph.

1920, I think Lawrence is in the New York Catholic Protectory as "inmate". Do you know how to verify if it is "my" Lawrence Heffernan in the Catholic Protectory?

1920 US Census Heffernan household:
John (53), Margaret (45), Joseph (17), George (16)

1915 New York Census:
Joseph (50), Margaret (43), Mary (18), Margaret (16), Helen (14), Joseph (13), George (12), Lawrence (9)

1900 US Census "Hefferman"
John (34, DOB Apr 1866), Margaret (28, DOB Dec 1871), Mary (3, DOB Jan 1897), Margaret V (9 mos, DOB Sept 1899)

I'm also interested in any baptismal records for the children and not sure if the parents married in US or Ireland.

According to 1920 Census they both immigrated in 1888
According to 1900 Census, John immigrated 1888, Margaret 1890 and they have been married for 5 years.

I would love to know where in Ireland they are from and of course, what their parents' names were. I found a Margaret Dignam in County Westmeath, Ireland online but I need to work backwards to determine if she's my ancestor. Of course Margaret is a common Irish name.

Birth certificates I think are or could possibly be the children of Joseph John & Margaret:
Sept 1 1906- #42682 Baby/Male Heffernan (Lawrence)
Aug 9 1905- #37385 Female Heffernan
Jun 25 1903- #28268 George Heffernan
Jan 23 1901- #5620 Ellen Heffernan (I think this is Helen on 1915 Census)
Sept 13 1899- #34628 Margret Heffernan
May 31 1898- #25387 Elizabeth Heffernan
Jan 22 1897- #5416 Elizabeth Heffernan (maybe Mary on 1900 & 1915 census)

I was not able to locate a birth certificate for Joseph Heffernan (aged 13 on 1915 Census, aged 17 on 1920 Census)

Grateful for any help!
Courtney Ferrara