Help finding Patrick Broe records B: abt 1877 D: 1948

Hi, 

Am have been trying for a while to find information on Patrick Broe, my gg grandfather. I have been told by my father that he was born in Dublin, but as he never met his g grandfather Patrick he knows no more than that. I would love to be able to ask my grandparents about any information they would have on him. But, they passed away some years ago. Before I took any interest in my family ancestry. I only wish I had asked more questions then. 

Anyhow, I have managed to find some records via Ancestry.co.uk. But, I am now stuck and confused. I am new to family history/ancestry. So I am hoping that someone on here will be able to help me by pointing me in the right direction. 

Here is what informtion I have...

Name: Patrick Broe (my gg grandfather) 

Born: abt  1877

Born in: Dublin (possibly? I have no sources to back this up. Only information handed down from my father)

Death: 1948

Died in: West Cheshire, Cheshire, England, UK.

I know at some point he/they moved over to England and settled in Wallasey, Cheshire, England, UK. 

Had a daughter...

Name: Marie Josephine Broe (my g grandmother)

Born: abt 1900

Marriage cert confirms the date of 1900. I can't find any birth record for her full name. Found one in Dublin for Sep 1901 for a Mary Broe, which could be a possibility? But, it doesn't give a mother's maiden name or forename. I have also searched for her in Birkenhead, Cheshire, England, UK and have found nothing for birth or cenus 1901 or 1911).

Marriage: Sep 1927 

Marriage: Birkenhead, Cheshire, England, UK.

Spouse: John Edward Price (B:1902 D:1967)

Her death: Mar 1956 

Died in: West Cheshire, Cheshire, England, UK. 

I do hope someone can help me. I am desperate to find out more  and I just seem to be hitting a wall now. I am also not sure if Marie may have been born Mary and changed her name later on in her life to Marie? 

I look forward to hearing some reponses.

Many thanks, 

Laura Fradley.