I'm a Welty descendant and would like to help straighten this up if possible.
I had correspondence with a descendant of Peter and Elizabeth Shulse a while ago. If I recall, they had a tradition that she was a Welty.
Abraham Welty was married first (by 1758) to Magdalena Gochenauer and second to Mary ?Roland. By the first wife he had Peter, Franey, Jacob; by the second he had David, John, Mary, and Abraham. He left a will in Rowan Co., NC, but didn't name the children. I've put them together by going through deeds, powers of attorney, tax lists, etc. His son Peter went to Fayette (later it became Clark) Co., KY, by 1787, and then moved to Warren (later it became Simpson) Co., where he died about 1824. Abraham's widow Mary and children Jacob, David, Mary, and John moved to the Bourbon/Nicholas/Montgomery Co. neighborhood in 1795.
Because they were all neighbors and members of the Dunker church, one researcher (Caroline Crabtree) hypothesized that Joseph Moler's wife was a Welty. But is there any other proof? I don't think he would have had two daughters with the same name.
Mary Welty died in 1826 and was buried in the Carter Cemetery in Nicholas County, KY. As her sons had left, she must have been near a daughter. One or more of the Shulse sons was in Cape Girardeau County, Missouri, in 1830, next to Abraham Welty's grandsons Daniel and Abraham. On the other hand, I can't find any later Moler-Welty connections.
I'd say that Elizabeth Welty married Peter Shulse and that Elizabeth, wife of Joseph Moler, was from a different family.