If that is all you know I can understand why you need help! A few more details such as the names of the daughters and possible ages would have been helpful. This may not be your family but is just a possibility.
There was an Eliza GILL who was living in Weston-super-Mare in 1881 with a son, William J GILL born in Weston in 1879, and a daughter, Emily E GILL born in 1881. Eliza GILL was born in Compton Bishop in about 1850 and she describes herself as the wife of a mason.
On the 1891 census she appears in Axbridge Workhouse with 3 young girls, Emily GILL, aged 10, Alice 7 and Annie GILL aged 5.
In the the records for Axbridge Workhouse it shows that Eliza GILL and her 3 daughters were admitted initially on March 16th 1891 but left again the same day. They were all readmitted on the 24th March 1891 which is how they come to appear on the 1891 census. Unfortunately I haven't got the discharge entries for later that year so I can't tell you when they left but that should be available from Somerset Archive Centre in Taunton.
Mrs E GILL and the three girls sailed to New York on board the Gallia on the 10th Dec 1892 from Liverpool. Do you have a marriage date for Eliza ?
This seems to fit your family but doesn't answer any questions about relatives of this family - However, you might be able to trace their father from Baptismal records - if William J GILL was born in 1879 in Weston-super-Mare, you might find him on later censuses.
This is my family. I have found out this much just recently. I don't know about Eliza's husband because in the 1881 census there is no man listed and the other two daughters were born after 1881., She supposely left the son William in England but never kept up with him, Did he survive and are there are relatives left if he did?
I'm afraid that this family is proving difficult to sort out without official documentation. Unfortunately I can't find a christening for any of them in Weston - perhaps they were non-conformist - but if you have seen the Workhouse records you will know that they are listed as Church of England.
It does look as if you will need a birth certificate of one of the children - perhaps William John GILL from FreeBMD
Births Sep 1879 GILL, William John Axbridge 5c 542
Or if you have a particular connection with one of the girls you might want to send for one of them instead - Emily Elizabeth GILL, Alice Maud GILL or Annie Maria GILL - they are all on FreeBMD.
On Ancestry someone has suggested that Eliza's husband was a stone mason born in Weston-super-Mare, Edwin GILL - and that she was Elizabeth BAWDEN (married in Burnham in 1869) but as this couple also turn up on the 1881 census in Lambeth this looks unlikely. Another has suggested that the father might be a Thomas GILL and Eliza's surname was CLARK - I haven't been able to find any proof of this either yet. Perhaps someone else can?
A warning about using published family trees - they may carry inaccuracies - and always need checking.
Another route would be to look for William John GILL on later censuses or burial records - it's strange that he doesn't appear to be on the 1891 census. There is a William GILL of the right age in a Certified Training School in Bristol in 1891 - he is said to have been born in Bristol but it might be worth checking out. If that was him it might explain why he didn't travel with the rest of the family - students at such a school had usually been in trouble with the police and sent there for a fixed term.
You are great. My grandmother was Emma Elizabeth Gill and her mother was Eliza Gill and so you have the right family with Clark. You could be right that Thomas Gill was in the school for troubled boys. What info can be gotten on that? My grandmother ended up at 99 years a wealthy woman with two good marriages so a happy ending but it appears that this side of the family was very troubled!!