Buddhism is also a science of worldly life. It's not only a science of liberation. I have faith (saddhā) you will find a good answer, but let's see what community says.
The answer to your question appears too vast to fully answer on this forum. However, you can start by reading the following link, which is both a summary & brief commentary on actual Pali sutta teachings about the science of relationship & worldly life.
A basic sutta about parents & children is Iti 106 With Brahma. As expressed in this sutta, it is obviously a scientific fact that "mother and father are very helpful to their children, they take care of them and bring them up and teach them about the world".
A sutta that discusses the Six Directions (Types) of relationship is DN 31 Sigalovada Sutta. The Sigalovada Sutta is extremely important in Buddhism; serving as the foundation for many South Asian Buddhist cultures in history (which have recently been eroded by the export of Western Corporate Imperialism masquerading as 'liberalism').
The Mātugāmasaṁyutta contains suttas about necessary qualities of women & men in marriage relationships.
In short, there are probably too many suttas to cite about the Buddhist science of relationships & worldly life, which is why I recommended to first read: A Constitution for Living: Buddhist principles [science] for a fruitful and harmonious life.
In the history of Western Buddhism, there were gurus who, immersed in promiscuity, overtly engaged in sexual misconduct with their students. These sexual abusers & often their impressionable students appear to not understand the science of relationship found in Buddhism. The Lokapala Sutta: Guardians of the World discusses this phenomena of being ignorant about how faithful relationships uphold/sustain the human world; to prevent the human world from degenerating into a world like that of instinct enslaved animals.
In Thailand, apart from the author of A Constitution for Living: Buddhist principles [science] for a fruitful and harmonious life, the most renowned scholar monk was Buddhadasa Bhikkhu. The first book Buddhadasa Bhikkhu compiled & published was called "Dhamma For Worldlings (Puthujjana)", which was for unenlightened householders who do not comprehend & are disbelievers in the Buddhist science of relationships.
In the Pali suttas, the word for 'disbeliever' is natthika, often translated as 'a nihilist'. The Pali suttas say the 'disbeliever' or 'nihilist' does not believe in the importance of the relationship & role of mother & father. The wrong view of a nihilist is expressed as follows in the Pali suttas:
Householders, there are some recluses and brahmins whose doctrine and view is this: ‘There is nothing given, nothing offered, nothing sacrificed; no fruit or result of good and bad actions; no this [human; humane] world, no other [degenerate] world; no mother, no father; no beings who are... spontaneously [arisen]; no good and virtuous recluses and brahmins in the world who have themselves realised by direct knowledge and declare this world and the other world.’ .... this... person is here and now censured by the wise as an immoral person, one of wrong view who holds the doctrine of nihilism
MN 60 - The Doctrine of Nihilism
In summary, comprehending the Buddhist science of relationship & worldly life requires the right practice of empathy. We discern the needs, hopes & wishes of others and therefore respond appropriately, morally & humanely to the needs, hopes & wishes of others.