Cambuslang's 3 miles SE of Rutherglen, I note. I haven't tried Allardice census records, because they don't show maiden names, and I've no first names to go on. I agree a relationship is likely, but I can't find it.
James Kilpatrick (b.1827) was dead by the time of 1881 census. He was a coal miner. His second son's birth certificate gives Coal-Miner; born at Fireworks, Parish of Govan. wife Jane Tennent, born in Rutherglen(prob. = Jean Tennant b. 12-May-1833) was alive in 1881; census & familysearch.org give these children: 1. William prob. named after maternal grandfather. 2. David Tennent b. 18-Oct-1855 almost certainly named after maternal grandfather (in which case maternal grandmother may have been Isobel Muir - not certain) 3. James named after father 4. Jane named after mother? or a grandmother (or both)? 5. William - name replaces earlier one who died young 6. Isabella named after ?? maybe maternal grandmother (Isabella=Isobel in Scotland) 7. John Allardice - mystery 8. Thomas Finlayson - same mystery