This excerpt is taken from Sheikh Muhammad Farooq's book Issues of the Two Eids.
When should the Opening Supplication (Du'a al-Istiftah) be recited?
There is no clear text regarding the timing of the Opening Supplication in the Eid prayer, but scholars differ on whether it should be recited after the Takbir al-Tahrima and before the additional Takbirs, or after the additional Takbirs but before the recitation.
Shafi'i School, may Allah have mercy on him:
Imam Shafi'i, may Allah have mercy on him, holds that the Opening Supplication should be recited immediately after the Takbir al-Tahrima, then the Takbirs of Eid should be said, followed by the Ta'awwudh (seeking refuge), and then the recitation.
Imam Ahmad ibn Hanbal, may Allah have mercy on him, position:
Imam Ahmad ibn Hanbal, may Allah have mercy on him, holds that the Opening Supplication should be recited after the Takbirs of Eid. Khilal preferred this school of thought, and Awza'i, may Allah have mercy on him, also agreed with this position because the Opening Supplication is connected to the Ta'awwudh (اعوذ بالله من الشيطان الرحيم پڑهنا), and the place of Ta'awwudh is before the recitation.
Abu Yusuf, may Allah have mercy on him, says: The Ta'awwudh should be recited after the Opening Supplication and before the Takbirs of Eid so that there is no confusion between the Opening Supplication and the Ta'awwudh.
Summary of the Discussion:
The summary of this discussion is that whichever method is adopted from the previous cases, it is permissible.
Reference: Al-Mughni by Ibn Qudamah, may Allah have mercy on him, with Al-Sharh Al-Kabir: 238/2
Because there is no clear text established on this matter, therefore, according to analogy and ijtihad, all cases are permissible.