You didn't name the girls you found in the 1901 census when you asked "what happened to the girls aged four and one?".

Brian Lawson's index to birth regts has:
SKILLICORN, William Ge[orge?] 8 Apr 1893 Dou 1021 SKILLICORN, William, OLLIER, Lydia
(not George William - but perhaps he was known as George).
SKILLICORN, James Edwa[rd] 6 Jun 1895 Dou 1161 SKILLICORN, William, OLLIER, Lydia.
SKILLICORN, Eleanor Ly[dia?] 20 Feb 1897 Dou 1283 SKILLICORN, William, OLLIER, Lydia.

BL's marriages have:
SKILLICORN, William 29 Jun 1890 D dsb 27a OLLIER, Lydia.

In the 1891 census they are in Conway, Wales: William 25 stonemason, b.IOM Douglas, wife Lydia 21 b.Cheshire Crewe, and boarder George Clague, S, 24, stonemason, b.IOM Castletown.
The previous household were at Castleview Hotel, and they were at "Do" (ditto) Cottage.
They were at Gateshead in 1901, as you saw.

FreeBMD has:
Deaths Dec 1904
SKILLICORN William 38 Gateshead 10a 621

Sue