In the Name of the Beloved
Unfortunately there are not many Shia commentaries of the Qur'an that have been translated into English. There are however a great number of Shia commentaries available in Arabic and Persian.
Translations in English:
Ali Quli Qaraee
The only complete Qu'ran Shia commentaries available English are: One thatis translated into English by Mir Ahmad Ali/Mahdi Pooya (http://al-quran.info/#home)and the other Noor ul Qur'an by Sayyid Abbas Sadr Ameli.
Some volumes of the Tafsir al Mizan by Allamah Tabataba'i have been translated into English.The English so far is around 12 volumes till Surah no. 5, verse 120.
Also some volumes of Tafsir al Namoonah, by Ayatullah Makarem Shirazi. The English so far is 5 volumes till Surah no. 44, verse 59.
There are also some commentaries of various Surahs in English, like Surah al Hujurat, Kahf, Yusuf etc. Some of these can be found at al-islam.org under the Qur'an and Hadith section.
The scholars also take into consider some Sunni commentaries as long as they are in accordance with the Qur'an and authentic hadith.
Some Arabic and Persion commentaries:
Al Mizan: Allamah Tabataba'i
Tafseer Namoonah: Ayatullah Makarem Shirazi
Majma ul Bayan: Fadh Ibn Hasan Tabarsi
Jawami ul Jami': Fadh Ibn Hasan Tabarsi
Tasneem: Ayatullah Jawadi Amuli
Noor: Mohsin Qara'ati
Tafseer al Qummi: Alai Ibne Ibrahim Qummi
Noor al Thaqalayn: Abd Ali Ibn Jumu'ah A'roosi Huwayzi
All the commentaries and translations of the scholars needed to be respected and appreciated. However, the matter of acceptance of what and what not is an expert material where scholars should be consulted.