Married in Lanark or Carmichael, Lanarkshire. Maybe the 1803 was young Alex's marriage; it certainly doesn't fit his parents in relation to him and his siblings.
"Helen or Jean" married Andrew or James Renwick, 1 June 1814 at Lesmahagow, producing children Andrew, Alexander, and Marion in Lanarkshire.
Agnes married John Brown, 9 July 1824 at Lesmahagow; son Alexander had 5 children while son John had 6.
Grace married Robert Swan; their daughter Jean married William (?) Crider, producing children John, Robert, and Grace; another daughter married a Mr Lyons, producing children Will, Samuel, Robert, Janet, Jean, and Annie; a son John was responsible for children Robert, Grace, Mary, Annie, Janet, John.
Alice married James or Andrew Bell; their daughter Annie married James K Percy and the family are thought to have been in Connellsville, Pennsylvania.
Most of the above ended up somewhere in Pennsylvania.
Nearly all of the descendant information was in a letter to a New Zealand relative setting out the various generations but with no mention of husbands' names, no dates, and scant information about places. Some tied up moderately well with IGI and other records. At least one descendant of a line other than the Pattersons (Diana Flanagan) has been contacted.