Although my sources seem to have disappeared:
First, the Khalkhas were not a coherent group. There was a lot of internal strife. Allying yourself with one Khalkha khan equaled a declaration of war to another. Both Tushiyetu Khan and Khan Shira were Khalkhas. Both reigned over a subset of the Khalkha population.
Originally Khalkha & Dzungars were allied. The Khalkhas and Oirats were in league, bound by the provisions of the Mongol-Oirat code. Read this for more information.
So Galdan Boshugtu Khan attempted to ally himself with Khan Shira, who got killed later on during an invasion by Tushiyetu Khan.
During the invasion of Tushiyetu Khan, Galdan dispatched his brother Dorji-jav with an army to support the remaining Khalkhas (at least the subjects of the late Khan Shira), but the alliance was defeated and Dorji-jav was killed in battle.
Following the loss of his brother & the war, Galdan Boshugtu Khan wanted to expand eastwards into the lands of Tushiyetu Khan.
So Galdan Boshugtu Khan allied himself with the Russians (already in conflict with Tushiyetu Khan) and invaded the Khalkha lands. After being defeated near Lake Baikal, Erdene Zuu Monastery, and Tomor, Tushiyetu Khan was forced to flee.
Following this conquest, the Qing Dynasty incited a revolt among the Khalkhas and supported Tushiyetu Khan. This lead to the Battle of Olgoi Lake (1688). The Khalkhas (with their allies) lost against Galdan Boshugtu Khan, which resulted in the remaining unconquered Khalkhas (including the spiritual leaders Jebtsundamba_Khutuktu & Zanabazar) to submit to Qing.
So to answer your question:
At the time of the Dzungar-Qing Wars, the Khalkhas were no longer a strong & independent faction. They were partially vassalized by Qing or under the reign of the Dzungar khans. No Khalkha force strong enough to tip the balance in the war existed.
Edit: Found the page Qing conquests of Mongolia, which explains it a lot better then I did.