Under what conditions can a husband abandon his wife ? What does scriptures say about this ?
According to Vashishta Dharma Sutras if the wife has sex with the husband's disciple or with his elders, in such extreme cases, the wife should be abandoned. Abandoning wife or husband unjustly are of course considered as sins.
If she commits adultery with an elder, however, she cannot participate in her husband’s ritual activities.
10 These four are to be abandoned: a wife who has sex with one’s pupil, a wife who has sex with one’s elder, especially a wife who tries to kill her husband, and a wife who has sex with a degraded man.
Vashishta Dharma Sutras 21.9, 10
Apparently, it is okay to divorce to focus on raising a child, as the seven Rishis did it. The wording is incredibly weird and really implies something else is going on, although I can't tell what. Probably okay for wives as well, without explicit mention of it not applying to them.
No one ever imagined that Svaha was the authoress of that mischief. But having heard that the (new born) male child was hers, she went to Skanda and gradually revealed to him the fact that she was his mother. And those seven Rishis, when they heard that a son of great power had been born (to them), divorced their six wives with the exception of the adorable Arundhati, because all the dwellers of that forest protested that those six persons had been instrumental in bringing forth the child.