The ancient Irish law system is known as Brehon Law and these laws remained customary in Ireland until the early 17th century. The overseers of these laws were the Brithem [written in English as Brehon] class who were the judges or arbitrators of the law.

The section of laws governing the subject of marriage and divorce are called the Cáin Lánamna [usually written in English as the Laws of Couples or Close Relationships]. In marriage both people retained their pre-marital property rights. There is no old Irish word for 'dowry' so this does not seem to have been part of the marriage rite. There was however a 'bride price' which the husband gave to the bride's father on marriage.

There are 14 reasons listed why a woman could divorce her husband and they are quite detailed as are the reasons given for a husband divorcing his wife. Yes, amongst them was the reason that if a man becomes too fat for intercourse his wife could divorce him. This is listed under the 'impotent' clause. But she also has the option of going to another man to become impregnated if she wants to and conceive a child and then return to her husband. Under these circumstances both of them would accept and raise the child as theirs.

At the divorce proceeding the marriage laws determined how property was to be split between the couple. It was the job of the Brehon to oversee the implementation of the law and judge the divorce settlement. Under the law he would determine who owned what property prior to marriage and thus keep it, what property they had jointly acquired in the marriage and how that properly was to be divided between them. This was partly determined by the amount of household work done by each partner in the marriage. If the marriage breaks up as a result of the husband's fault the bride's father can retain the bride price. If the fault lies with the bride, it must be returned to the husband. All of this would be determined by the Brehon in charge of the case who might rely on his own perception in applying the law or seek testimonials from family members.

Edit: Clarification

Sources: A Guide to Early Irish Law by Fergus Kelly.

Donnchadh Ó Corráin in Marriage in Early Ireland ed Art Cosgrove.