The Rig Vedic Verse 10.82 mentions Tvashtar emanating from Vishwakarman but thats not all. There are different layers to this enigmatic god depending on which scriptures you read. The Vedic Tvashtar is described in various hymns as the artist who creates an embryo inside a woman's womb.
Atharva Veda Book 5 Hymn 25 mentions the following:
4-5 Let Mitra-Varuna and God Brihaspati lay the germ in thee. Indra and Agni lay the germ, Dhātar bestow the germ in thee. Let Vishnu form and mould the womb, let Tvashtar duly shape the forms.
11 Tvashtar, celestial artist, lay within the body of this dame. A male germ with the noblest form for her in the tenth month to bear.
Book 29 Verse 9 of Shukla Yajurved mentions something similar:
9 The God-devoted son Tvashtar produces: from Tvashtar springs to life your fleet-foot Courser. Tvashtar gave being to this All about us. Priest, worship here the mighty work's achiever.
He is even invoked in Atharva Veda Wedding Hymn for he created both the male and the female forms:
Tvashtar formed her to be thy dame, Tvashtar made thee to be her lord. Long life let Tvashtar give you both. Let Tvashtar give a thousand lives.
Rig Veda Book 3 Verse 55 also mentions something to that effect:
19 Tvaṣṭar the God, the omniform. Creator, begets and feeds mankind in various manner. His, verily, arc all these living creatures. Great is the Gods’ supreme dominion.
Additionally, the Vedas also make him the father-in-law of Surya. As mentioned in Rig Ved Verse 17.1 of Book 10:
Tvashtar prepares the bridal of his Daughter: all the world hears the tidings and assembles. But Yama's Mother, Spouse of great Vivasvān, vanished as she was carried to her dwelling.
RV Book 10. Verse 10.5 also mentions him as the creator of Yama and Yami, the offspring of Surya and Saranyu referring to his dual role as the fashioner of embryos as well as their forefather:
Even in the womb God Tvaṣṭar, Vivifier, shaping all forms, Creator, made us consorts. None violates his holy ordinances: that we are his the heavens and earth acknowledge.
Tvashtar also sired Trisiras or Vishwaroop as well as created Vritra. His being the father of Trisiras is also mentioned at multiple places one example being:
Well-skilled to use the weapons of his Father, Āptya, urged on by Indra, fought the battle. Then Trita slew the foe seven-rayed, three-headed, and freed the cattle of the Son of Tvaṣṭar.
Lord of the brave, Indra cleft him in pieces who sought to gain much strength and deemed him mighty. He smote his three heads from his body, seizing the cattle of the oniniform (Vishwaroop) Son of Tvaṣṭar.
Paradoxically, he also created the Vajra with which Vritra was slayed as discussed in this question that was answered by you. Now all this is as per the Vedas and we get corroboration of some of this in the Mahabharat. Section 9 of Udyog Parva mentions the relationship between Tvashtar and Trisiras/Viswaroop as well as Vritra:
Once Twashtri the lord of creatures and the foremost of celestials, was engaged in practising rigid austerities. And it is said that from antipathy to Indra he created a son having three heads. And that being of universal form (Viswaroop) possessed of great lustre hankered after Indra's seat.
After Indra kills Vishwaroop the enraged Tvashtar creates Vritra to avenge his son's death and this text does not mention that he created the Vajra:
Now when the lord of creatures, Twashtri, heard that his son had been slain by Indra, his eyes became red with ire, and he spoke the following words, 'Since Indra hath killed my son who had committed no offence at all, who was constantly engaged in the practice of austerities, who was merciful, possessed of self-control, and of subdued passions, therefore, for the destruction of Indra, I will create Vritra.
The Purans however add a different perspective by mentioning THREE different origins of Tvashtar. Vishnu Puran Book 1 Chapter 15 mentions the following:
There were twelve celebrated deities in a former Manwantara, called Tushitas, who, upon the approach of the present period, or in the reign of the last Manu, Chákshusha, assembled, and said to one another, "Come, let us quickly enter into the womb of Adití, that we may be born in the next Manwantara, for thereby we shall again enjoy the rank of gods:" and accordingly they were born the sons of Kaśyapa, the son of Maríchi, by Adití, the daughter of Daksha; thence named the twelve Ádityas; whose appellations were respectively, Vishńu, Śakra, Áryaman, Dhútí, Twásht́ri, Púshan, Vivaswat, Savitri, Mitra, Varuńa, Anśa, and Bhaga.
Chapter 25 of Book 1 of Vishnu Purana calls him the son of Vishwakarma, who himself is the son of Vasu Prabhas and Yogasiddha, the sister of Devguru Brihaspati:
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.
According to Section 1.3.23 of the Shiva Puran he brings the bones of Dadhichi to his father Vishwakarma to create the Vajra for Indra:
Dadhichi Gave up his life by his yogic power. Indra then instructed Kamdhenu to extract the bones from the dead body of Dadhichi. The bones were on given to 'Twashta' to construct the weapon-Vajra. Twashta took the weapons to Vishwakarma who at last constructed the Vajra.
Furthermore, the Upodhgata Pada of the Brahmanda Purana mentions him as a son of Shukracharya:
Since a person with the same name is mentioned as an Aditya, then as the son of Vishwakarma and then as the son of Shukracharya, therefore I am inclined to think that Tvashtar, just like Indra may actually be a title that is why we have different stories about him!
The Vedic Tvashtar however, corresponds most closely to the Puranic Vishwakarma based on the common achievements of both.