Tarawih is a blessed prayer which Muslims perform during Ramadan and is highly rewardable from Allah the Almighty. It is included in Qiyam-ul-Layl (offering mandatory prayer at night) in which the Prophet (peace and blessings of Allah be upon him) said, “Whoever observes optional prayer at night during Ramadan out of faith and in the hope of reward, his previous sins will be forgiven.” (Related by Al-Bukhari and Muslim) Thereupon, every Muslim, man or woman, should observe it and to have patience in order that Allah forgives them their sins as stated by the Hadith.
Muslims are required to follow the imam (leader in congregational prayer) in prayer, in accordance with the Prophet’s saying, “The imam has only been appointed to be followed, so do not differ from him.” The Hadith indicates that a praying person should take after his imam in order to avoid troubles and dissensions, especially for the matters that were basically liable to differences among scholars and they gave different views as regards these issues.
With regard to raising hands while saying Qunut, scholars have two different views. The Shafi`is believed that it is recommendable, which was adopted by Ahmad, Ishaq and Hanafis. Malik and Al-Awza`y viewed that it is not so claiming that there is no proof for this. However, the opinion of the majority of scholars is to raise hands in Qunut. All in all, you are advisable to follow your imam in this concern as he relies on a reliable view of a school of Fiqh which is of Malik and Al-Awza`y.
As a Muslim in this condition you are required to follow your imam in the prayer even if you are adopting another way of prayer in order to avoid difference and dissensions. It is related that the great scholar Al-Shafi`i once visited the mosque of Imam Abu Hanifah and he performed Fajr (Dawn) Prayer according to the madhab of Abu Hanifah with regard to Qunut and other acts of prayer that he may hold another view regarding them.
As for the witr prayer, it is permissible to go home and offer witr prayer in congregation with relatives, it is even preferrable.