As an analogy, you are asking what does the Chemistry textbook say on how you should behave with your teacher and with other students when you are in the chemistry lab. You won't find it in Chemistry textbook, but you will find it in the university rules & regulations manual. And depending on which university it is (i.e. on which kingdom/empire/county it is), such rules change. So before we wonder whether something is or is not covered in vedas, you need to first analyze whether that thing is vulnerable to changing times and eras. If it is, then you will not find any suggestion on it in vedas. Apart from this, the only other prescription you would find in vedas is on how to conduct yagnyas.
Having thus clarified why you will not find a suggestion on this topic of societal/civilizational construct of social norms/code of conduct in vedas, while veda does not concern itself with how they should behave etc., we can nevertheless see glimpses of how ancients of the old behaved with their fathers/parents. That is provided below:
First of all, in Vedas, the term father is almost always used to denote the heaves (dyaus) or Agni & Rudra, and occasionally Indra, Varuna, Prajapati & Soma depending on context of the sukta.
I. In Rik veda, 4th mandala, hymn 18.9 & 12. we see that Indra killed his own father:
And Vishnu does help him kill vritra thereafter.
II. In Rik veda, 6th mandala, hymn 44.22, Soma/Indu stole away weapons from his bad father and spoiled his bad father's tricks:
22. This God, with might, when first he had his being, with Indra for ally, held fast the Paṇi. This Indu stole away the warlike weapons, and foiled the arts of his malignant father.
III. In Rik veda, 10th mandala, hymn 100.5 sort of defines who is a father, as
5. Indra hath given the body with its song and strength: Bṛhaspati, thou art the lengthener of life. The sacrifice is Manu, Providence, our Sire. We ask for freedom and complete felicity.
Sire means father. Underlying assumption in verse, is that a father is he who ensures providence. So we need to understand that a father who does not provide to his kids, is no father. Think of a modern family where mother is the bread winner in home and father is a stay-at-home who focuses on raising kids.
IV. In Rik veda, 10th mandala, hymn 124, which is an euology to Agni & Indra, seems to grant freedom to sort of treat God as your father in lieu of your biological father:
4. I tarried many a year within this altar: I leave the Father, for my choice is Indra.
Away pass Agni, Varuṇa and Soma. Rule ever changes: this I come to favour.
V. In Yajur Veda, 6th kanda, 5th hymn, one duty/obligation of father & son are mentioned as an analogy:
The Agrayana is the father, the tub is the son; if the Agrayana is exhausted, he should draw from the tub; that is as when a father 2 in destitution has recourse to his son. If the tub is exhausted, he should draw from the Agrayana; that is as when a son in destitution has recourse to his father.
So it seems it is a father's obligation to care for his son when his son is going through bad times, and vice versa, regardless of age.
Please understand that the reason why the dharmashastras (Smirits & Sutras) laid down the social norms between children & parents, is for one purpose --- civilizational building and civilization maintenance. And reason why such social tradition/norms rose requiring children to keep blind obedience to the father is because:
Fathers back then taught their children shastras (vedas or smritis or dhanur, or ayur or etc. depending on varna), so children's guru was their father.
Children livelihood was inherited from fathers, so childrens yajamana or employer was also their fathers only. Thus a son well into his own family life with his wife & kids was still living in the home of his forefathers and his own old & alive father was still the employer & thus head of household. As he is providing the son with shelter & food & income, how can a son NOT be obedient & loyal to his father?
Today, those roles are not fulfilled by fathers anymore (for various reasons of course, not fathers' fault in that sense but their fault too since they voted to bring about these forms of govt. and today's social changes), instead today children have their separate gurus (teachers & professors in schools & colleges) and have separate employers, so my take is that today childrens' first allegiance/obedience needs to be to their employer for he/it provides sustenance and livelihood to children; and second allegiance needs to be to their teachers/professors, and finally last allegiance to their own biological parents.