<He would have liked to have all the family together in one big reunion before he died
It is not incorrect to use a modal and an infinitive perfect forms.
Would have liked already expresses that what is in consideration has not materialized.
For this reason, to have had is unnecessary, but not incorrect.>
How about in examples such as this, Incho?
He would have liked to have seen all the family together in one big reunion before he died.
He would have liked to have brought all the family together in one big reunion before he died.
He would have liked to have gathered the family together in one big reunion before he died.
Would you also omit the verb after the second "have" in each of those?