Answer
The Bhagavad Gita is a scripture of liberation in the midst of duty. It is a text of synthesis (samanvaya-shastra).
The Ashtavakra Gita is a scripture of direct Advaita (non-dual) realisation. It is a text of incisive Self-knowledge.
The Uddhava Gita is a scripture of comprehensive spiritual guidance accompanied by devotion and renunciation. It is an extensive compendium of teachings.
Now understand a practical truth: the more scriptures you read, the more your doubt may increase. In Hinduism, there are not one or two but hundreds of scriptures: four Vedas, 108 Upanishads (which have been counted up to 200), numerous Smritis including the Manusmriti, 18 Mahapuranas, 18 Upapuranas, more than 300 Agama texts, approximately 100 Ramayanas, the Mahabharata, and hundreds of texts belonging to various sampradayas (traditions). It is for this very reason that the greatest confusion also arises in many people's minds regarding Hinduism.
It is precisely for this reason that in Bhagavad Dharma, a decision was made that our foundational scripture would be one alone: the Bhagavad Gita, which is regarded as the direct word of God. And to understand the ideas of the Bhagavad Gita in greater detail, two supporting texts were chosen:
1. In the Itihasa (historical epic) tradition: the Ramcharitmanas of Tulsidas. 2. In the Purana tradition: the Bhagavata Purana.
But these too, only to the extent that they do not contradict the Bhagavad Gita — because both are the utterances of saints, not the direct speech of God. Therefore, there was no need seen to wander beyond these three.
Let me also explain a technical point. In every religion, there is a classification of scriptures:
Primary Canon: the primary scripture. Secondary Canon: the secondary scriptures. Tertiary Canon: the tertiary scriptures.
In the context of Hinduism, only two can principally be placed in the Primary Canon: the Vedas (including the 10–12 ancient Upanishads that form their knowledge-portion) and the Bhagavad Gita. The Vedas contain a larger portion of hymns and ritualistic content, with relatively less doctrinal analysis. Therefore, for understanding doctrine in an organised manner, the Bhagavad Gita becomes the central text.
In the Secondary Canon come certain Mahapuranas, the Ramayana, and texts such as the Manusmriti. The majority of the remaining texts are placed in the tertiary category.
In Christianity, the Bible is the Primary Canon. In Islam, the Quran Sharif is the Primary Canon. After that, certain principal Hadith collections such as Sahih Bukhari and Sahih Muslim are regarded as Secondary Canon, and various other Hadith collections are considered tertiary. Priority is given to the Quran. Where a matter is not clear in the Quran, the secondary texts are consulted. Generally, there is no need to go beyond the Quran and a few select principal Hadith collections.
Likewise, for understanding life and spirituality, the Bhagavad Gita is the foremost scripture. The 10–12 principal Upanishads from the knowledge-portion of the Vedas may also be read, but they contain nothing that falls outside the essential metaphysical teaching of the Gita. Where a deeper clarification of any verse of the Gita is needed, assistance may be taken from the Ramcharitmanas and the Bhagavata Purana.
For those who are dharma-teachers, academics, or researchers, the reading of additional texts may be useful — such as the Shiva Purana, the Devi Bhagavata Purana, and so on. But for the ordinary seeker, it is a matter of simple common sense: when everyone accepts the Bhagavad Gita as the word of God, how can the Gita of Rishi Ashtavakra serve as a foundational scripture on par with the Bhagavad Gita?
As for the Uddhava Gita, it provides detailed teachings particularly from the standpoint of devotion. If you find any point in it that appears to contradict the Bhagavad Gita, please point it out; it will be resolved.