H Dollond-Hulke doesn't show up on the genealogy websites, but Henry Dollond Hulk - without the terminal "e" - does. He was born in Brixton in 1885, the son of Abraham Hulk and his wife Blanche, née Werninck. Abraham, born in Amsterdam in 1844, was a member of a large Anglo-Dutch family of artists who pursued their careers in both Britain and the Netherlands. His father, also called Abraham, was a marine painter, but Abraham Jnr also painted landscapes.
Henry's family moved around quite a lot - they were in Willesden in 1891, Nottinghamshire in 1901 and Henley in 1911. Henry D Hulk is recorded under that name in the census of 1911, with his profession given as "painter (artist)". By the time of their deaths, Henry, his three brothers and an unmarried sister were all recorded as "Hulke". Perhaps the "e" was added during the First World War in an attempt to give the name a less Germanic look (though to me the effect is quite the opposite). He was presumably the Henry D Hulke who died in Dover, aged 83, in 1968.
His brother Frederick Martinus signed his work "F. Martinus Hulk". I suspect that the painter who signed "Claude Hulke" was another brother, William Claude (1878 - 1955).