Should the ruler be obeyed if he commands that the Prayer for Rain (Salat al-Istisqa') be performed immediately after the Friday Prayer (Salat al-Jumu'ah) in the mosque, so that they pray Jumu'ah and then perform the two rak'ahs of Istisqa' thereafter?

Obeying the ruler is obligatory unless he commands disobedience. If he commands the performance of Salatul-Istisqa (prayer for rain) after Jumu'ah prayer, then obedience to him is obligatory because the majority of scholars consider it permissible to perform it at any time other than the times of disliking (makrooh), and the time after Jumu'ah is not among them. Even according to the view that it is disliked after Jumu'ah, some jurists hold that the ruler should be obeyed in this matter, especially since the disliking is not unanimously agreed upon. The Imam should pray the two rak'ahs of Istisqa after Jumu'ah and then deliver two sermons. If he suffices with only the two rak'ahs, it is permissible, as the sermon after Istisqa is supererogatory (mustahabb) and not obligatory.