Is Sending Blessings upon the Prophet in Tashahhud Mandatory?
Question

During Tarawih prayer the Imam very quickly says Taslim. I do get enough time to finish the first Tashahhudd. But he said Taslim before I could start the second Tashahhudd. Is it alright if I finish the prayer at that point? Or is the second Tashahhudd compulsory?
Praise be to Allah.Scholarly Opinions on Sending Blessings upon the Prophet in the Tashahhud
The scholars differed concerning the ruling on sending blessings upon the Prophet (peace and blessings of Allah be upon him) in the Tashahhud in prayer . There are several opinions, one of which is that it is a pillar or essential part of the prayer, without which the prayer is not valid. Others said that it is obligatory, and the third view is that it is Sunnah and recommended, but is not obligatory.
Shaykh Muhammad As-Salih Al-`Uthaymin (may Allah have mercy on him) regarded the third view as most likely to be correct. He said in his commentary on Zad Al-Mustaqni’:
The words “Sending blessings upon the Prophet (peace and blessings of Allah be upon him)” mean, in the last Tashahhud, which is the twelfth “pillar” of the prayer.
The evidence for that is the fact that the Companions asked the Prophet (peace and blessings of Allah be upon him): “O Messenger of Allah, we have learned how to send Salams upon you , how should we send blessings upon you?” He said: “Say: Allahumma salli `ala Muhammad, wa `ala ali Muhammad (O Allah, send blessings upon Muhammad and upon the family of Muhammad).” A command implies that it is obligatory, and the basic principle concerning an obligation is that it is a mandatory, and if it is not done, then the prayer is invalid. This is how the jurists (may Allah have mercy on them) settled this issue.
But if you think about this Hadith, it is not obvious therefrom that sending blessings upon the Prophet (peace and blessings of Allah be upon him) is a “pillar” of the prayer, because the Companions were simply asking how to do it – how should we send blessings upon you? So the Prophet (peace and blessings of Allah be upon him) taught them how to do it. Hence we say that the command in the word “Qulu (Say)” does not mean that it is obligatory; rather the purpose here was to teach them. If there is any other evidence which enjoins sending blessings upon the Prophet (peace and blessings of Allah be upon him) in prayer, then it must be followed; if there is nothing apart from this report, this does not indicate that it is obligatory, let alone indicating that it is a “pillar” of the prayer.
Hence the scholars differed concerning this matter and there were several opinions:

The first opinion is that it is a “pillar” of prayer. This is the well-known view of our Madhhab, that prayer is not valid without it.
The second view is that it is obligatory, but is not a “pillar”, and the prostration of forgetfulness (Sujud As-Sahw) is required if it is omitted by mistake.

They said: That is because his words, “Say: Allahumma salli `ala Muhammad, wa `ala ali Muhammad (O Allah, send blessings upon Muhammad and upon the family of Muhammad)” imply both a command and teaching, and we cannot say that it a “pillar” of the prayer without which prayer is not valid when it possible to understand the phrase as meaning that it is an obligatory part of prayer and not a “pillar”.
3.The third view is that sending blessings upon the Prophet (peace and blessings of Allah be upon him) is a Sunnah, and is not obligatory or a pillar of the prayer. This view was narrated from Imam Ahmad. If a person deliberately omits it, his prayer is still valid, because the evidence quoted by those who regard it as obligatory and those who regard it as a pillar of the prayer does not clearly indicate either of the things suggested, so the basic principle is that it is not essential.
This is the view which is most likely to be correct because there is no other evidence apart from this report which the jurists (may Allah have mercy on them) quoted as evidence. We cannot regard an act of worship as being invalid because of evidence which may be understood as a command or may be understood as teaching. (End quote from Ash-Sharh Al-Mumti`, 3/310-312)
Based on this, a prayer offered without it is still valid.
Guidelines for the Imam: Balancing Speed and Perfection
This Imam and others who rush through Tarawih prayers in a negligent manner, thus preventing those who are behind them from completing their prayers, should be advised.
The scholars have stated that the Imam should perform the prayer slowly so that the members of the congregation can perform the obligatory parts and some of the Sunnahs ; it is disliked to hasten so much that the members of the congregation are not able to do that.
An-Nawawi (may Allah have mercy on him) said:
The meaning of the Hadiths – i.e., the Hadiths which tell the Imam to make the prayer light – on this topic are clear, which is the command to the Imam to make the prayer light without omitting or falling short in any of the Sunnah actions of prayer.
It says in Al-Mawsu`ah Al-Fiqhiyyah (14/243):
What is meant by making it light is keeping it at the lowest level of perfection, so he should do the obligatory parts and the Sunnahs, and not only do the least possible parts of the prayer or do it in the most perfect manner.
Ibn `Abd Al-Barr (may Allah have mercy on him) said:
It is unanimously agreed among the scholars that it is recommended for the Imam to make the prayer light, i.e., at the lowest level of perfection, without omitting or neglecting any part of the prayer. Then he said: I do not know of any differing opinion among the scholars concerning the fact that it is recommended for everyone who leads the people in prayer to make the prayer light so long as it is still complete.
Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni (1/323):
It is recommended for the Imam to recite Quran, Tasbih and the Tashahhud in as slow a manner as one who is reciting it slowly behind him, and he should make his bowing and prostration as long as he thinks that the old, young and heavy need. If he does not do that, and he does it at his own pace without paying attention to the people behind him, it is disliked but is still sufficient.
In Al-Mawsu`ah Al-Fiqhiyyah (6/213) it says:
It is disliked for him to rush so much that the one who is praying behind him cannot do the Sunnah, such as saying the Tasbih three times when bowing and prostrating, and completing the Sunnah words in the final Tashahhud.
Shaykh Ibn `Uthaymin said in an essay on the rulings on fasting, Zakah and Tarawih:
With regard to what some people do, hastening too much, this is contrary to what is prescribed in Shari`ah, and if he does it to such an extent that he omits an obligatory or essential part of the prayer, then it invalidates the prayer.
Many Imams do not perform Tarawih prayer in a deliberate manner, and this is a mistake on their part, because the Imam is not praying for himself only, rather he is praying for himself and others. He is like a leader who is obliged to do that which is in the best interests of all. The scholars stated that it is disliked for an Imam to rush in such a way that he prevents those praying behind him from doing what they are obliged to do. (End quote)
And Allah knows best.