Publisher's rights after author renewed copyright

[4075mva]

I have written a sequel to the utopian novel Islandia (published 1942). The heirs of the author have owned the copyright since 1958 and renewed it in 1970. When I contacted them for permission to base a sequel on the original work, the family has mentioned that I will have to deal with the publishers. The last version of the novel was published by Overlook Duckworth, by permission of Henry Holt and Company. Does the publisher have rights I would also need to obtain in order to quote the original novel?
(The family has not yet given me permission while all the extended members read my draft.)