I think the children that you found, William and sister Catherine, likely this entry in 1891 Bathgate:
Alexander Wilson 40 oil work lab. b. Ireland
Elizabeth A Wilson 42 b. Ireland
William J Wilson 13 b. Johnstone, Renfrewshire
Catherine A Wilson 12 b. Johnstone, Renfrewshire
Ellen Wilson 10 Johnstone, Renfrewshire
Mary Jane Wilson 8 Johnstone, Renfrewshire
Alexander Wilson 4 Uphall West Lothian
Address: 61 Cochrane St, Bathgate
The other entry you mentioned from 1881, not sure who James is son of, but I think this is the entry:
Elizabeth Wilson 68 Formerly Hand-Loom Weaver b. Johnstone
Peter Wilson 36 son Elderslie, Renfrewshire
James Wilson 32 son Engineer at Works b. Elderslie, Renfrewshire
William Wilson 12
James Wilson 10
Annie Wilson 8 ?
https://familysearch.org/pal:/MM9.1.1/FQZK-7JCMartha Wilson 6 ?
https://familysearch.org/pal:/MM9.1.1/FQ46-GHJWilliam Wilson 4
Address: 9 High Street, Johnstone, Paisley Abbey
Not sure if William and James were born to other children for Elizabeth Snr.
Monica