You don't seem to have looked at the IGI on FamilySearch.org. Richard Pemberton was born 24/2/1818, baptised 8/3/1818 Dumbarton, son of John Pemberton and Mary Gilderoy. His parents married 29/5/1807 Dumbarton and other children are: Margaret b.27/6/1812, bp.12/7/1812, Susan b.13/4/1810, bp.18/4/1810, Elizabeth b.1/2/1822, bp.17/2/1822, Thomas b.13/5/1816, bp.19/5/1816, Timothy b.11/7/1825, bp.7/8/1825, John b.28/5/1808, bp.19/6/1808, William Price b.10/2/1820, bp.29/2/1820 and Eleanor b.3/5/1823, bp.18/5/1823.
Looks like John senior had died by 1841.
1841 Census - High Street North Side, Dumbarton
Mary Pemberton 50 IND born Scotland
Margaret Pemberton 25 ditto
William Pemberton 21 ditto
Elinore Pemberton 17 ditto
Timothy Pemberton 15 ditto
By 1851 Mary appears to have died
1851 Census - High Street, Dumbarton
Margaret Pemberton Head 35 Dressmaker b. Dumbarton
Eleanor Pemberton Sister 23 Dressmaker b. Dumbarton
Richard Pemberton is not actually listed twice on the 1851 Census. They are 2 different people. The IGI shows that a Richard Pemperton (later Pemberton) was baptised 26/5/1816 Hunslet, Yorks. son of Richard and Susanna. In 1841 this second Richard is living in York (born Yorkshire) - the Richard you found in Scotland in 1851 is shown as born York, England and is therefore the one born Hunslet.
Annette