Thank you both for your replies. I see what you mean jtas about Mary not being present for George's death while being present for her daughter's in May. She doesn't appear to be present either for her other daughter who died later in Sept, in Ireland, of that year. I find it hard to take in myself that Mary lost three of her immediate family in the year 1888. I did try looking generally at passenger lists before but didn't really come up with anything much. I must admit I wasn't sure what passenger ferry and what route to look up.
With Mary's off spring I did find a George Goodman on The Caronia, in June 24th 1923 (?junior). This person was born in 1881 aged 42 years. Liverpool England port to New York. I did discount it as my George (junior) would be only be 41 years as his birthday was not until the 4th July. It didn't give info as to where he was born. He was there again doing that crossing in July and August. I think he may have been working on the ship as a hairdresser. Unrelated, (but sometimes occupations are repeated in families), my dear departed dad was a barber and his sister trained to be a midwife at the rotunda but she dropped out. Mary Goodman (McCarthy) may not have been alive then. She is supposed to have died in the county home (mainly for poor people) in 1933.
Re her maiden name her family may have put the Mc in front of the name I am not sure about that. Equally the person writing down the name may have used the easier pronunciation. I believe that was common when Irish folk had to pronounce names that were not strictly of Irish origin. For instance my Dodgson ancestors, in Ireland on one census were referred to as Dobson! In the past when some of my older relatives from the countryside were alive I have actually heard them refer to that family as Dobson.