The family is included in the 1881 Little Hulton, England, census; it appears it was enumerated on or before July 20, 1881. Alice's birth year is given as about 1858 and George about 1855.
Did Alice remain in England?
Who were the other relatives who traveled to the US? Names, ages, when they went to the US and where they lived? This might help in a search for the family.
The occupation of coal miner might help narrow down where George and Alice and family lived in the States.