Thanks for following up with this family. I believe this is indeed my 4 x great-grandmother Barbara Sørensdatter in the 1840 census, but the others in the household appear to be unrelated to Barbara.
Peder Hansen (who died in 1828) and Barbara had two sons and no daughters. Hans Peter Petersen, born in 1797 and baptized in Hostrup, was the elder. He was a cottage farmer and glazier who married Ellen Jürgensen of Jundewandt, Tønder in 1822. They had nine children, two of whom were my great-great-grandfathers.
The younger son Adam Lautzen Langer Petersen, born in 1806, was a farm laborer who never married.