Ref. No. 38 / 1158
In the name of Allah the most Gracious the most Merciful
The answer to your question is as follows:
Reading dua between the two sajdas is narrated in ahadith. Hence it is allowed to read the dua. But for imam, it is not desirable to read it in congregational prayer as it may lengthen the prayer and cause difficulty to weak, old and sick people in congregation while a hadith says "If anyone of you leads the people in prayer, he must make it light" And Muqtadi (follower) also should not read the dua as he has to follow the Imam properly.
Nevertheless for Munfarid (person offering Salah individually), it is a preferable act to read the dua regardless of the prayer being a farḍ (obligatory) or a nafl (voluntary) prayer.
And Allah knows best
Darul Uloom Waqf Deoband