I have a family with two disabled children. Came here from India in 2006. Father is here on a highly skilled migrant visa, works as a Paediatrician. Mother has no recourse to public funds, not sure about father. Both children born in India, one born with a disability, the other developed later on. I know they won't be able to claim CB or CTC but is there any possibility of claiming DLA for the children?

DLA is public funds, so the question is not whether either of the parents is able to have recourse to public funds, but whether the children can do so. You cannot have recourse to public funds if you are subject to immigration control, which essentially means having a limited visa. If the family as a whole is able to apply for indefinite leave to remain, the bar on public funds is usually lifted.