Srimad Bhagvatam tells us the story about Vritra's elder brother Vishwarupa who was killed by Indra because he used to give some portion of the Yagya oblations to the Asuras to whom he was related through his mother. Can any one tell me who was his mother and how exactly was she related to the Asuras?
Before getting to Trishiras I have to mention a little more about his father Tvashtar. here are various interpretations of who really Tvashtar was and you can check the evidence as shared in the answer to this question. According to Vishnu Puran Book 1 Chapter 25:
The sister of Váchaspati, lovely and virtuous, Yogasiddhá, who pervades the whole world without being devoted to it, was the wife of Prabhása, the eighth of the Vasus, and bore to him the patriarch Viswakarmá, the author of a thousand arts, the mechanist of the gods, the fabricator of all ornaments, the chief of artists, the constructor of the self-moving chariots of the deities, and by whose skill men obtain subsistence. Ajaikapád, Ahirvradhna, and the wise Rudra Twasht́ri, were born; and the self-born son of Twashtri was also the celebrated Viśwarúpa.
The Vayu Purana omits the intervening Vishwakarma and makes Tvashtri directly the son of Prabhas and Yogasiddha:
So according to this text, Tvashtar's wife, the mother of was the daughter of Prahlad and the sister of Virochan. This is the only relation I could find of Trishiras with the Asuras through his mother. If I find something else I will add the references.