Halldór Pálsson (1878-1933) had 7 children.The last of those died in 2002, but many of his grandchildren are alive in Iceland.
Jóakim Pálsson (1879-1914) had 8 children.Most of his descendants live in the Reykjavík area, but there are a few around Hnífsdalur (NW Iceland)
Páll Pálsson (1883-1975)had 7 children, one of which is still alive.Their descendants are also either around Reykjavík or around Hnífsdalur.
Margrét Pálsdóttir (1884-1973) never married and had no children.
Sigríður Pálsdóttir (1889-1930) had 5 children, one of which is alive.Sigríður Aðalsteinsdóttir was indeed another of her children, but she died childless in 2003.
Now, regarding the brothers and sisters of Helga Jóakimsdóttir, Aðalbjörg and Sigríður emigrated, as did the widow of Aðalbjörn and their children.Páll has no living descendants, but the was a final brother, Jóakim who stayed behind.He married 4 times, but only had one child who reached adulthood, Tryggvi Jóakimsson and he has a few descendants in Iceland.
Anyhow...I siggest you contact Aðalsteinn Geirsson.He is the son of Aðalbjörg, who was the daughter of Jóakim who was the son of Helga (see above).You can reach him at firstname.lastname@example.orgI just called him, and he is expecting an e-mail from you.