Is the wife sinful if she refuses to bear children—despite her husband's request—due to living in her parents' cramped house, the husband's prolonged absence, and her father's refusal to allow her to leave the house?

Procreation is a shared right of both spouses, and neither of them is permitted to prevent the other from it without a valid excuse. The wife's staying at her family's home is not an excuse that permits depriving the husband of procreation. If the family's home is cramped, the wife has the right to demand a suitable, independent dwelling. The father does not have the right to prevent his daughter from living in a house that her husband approves of, for obedience to the husband takes precedence over obedience to the parents.