This looks like a better match and there is a gap in the children's ages. Could it be John brown was married previously

1861 Bothwell Lanarkshire - all the children were born Lanarkshire.
John Brown 40 Born Lanarkshire. Coal-Miner.
Jane Brown 32 Born Tyrone. Ireland.
John Brown 16 Ann Brown 10
Mary Brown 4 William Brown 3
Margaret Brown 1
Mary Little 55 Visitor. Born Tyrone Ireland.
Twinkles