Book of Hosea Chapter 2 Vs. 4

 Israel's Unfaithfulness Punished

And I will not have mercy upon her children; for they be the children of whoredoms. Hos. 2:4

not have mercy... The children are like their mother: not only are they born of doubtful parentage, but are personally defiled. Not only is idolatry enshrined in the national sanctuary and the royal palace, but the people love to have it so. They endorse the degradation of their mother.

God greatly blesses the children of those who are faithful to Him. Let us see what happened to those who worshipped false gods.

Exodus 20:5 "Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God [am] a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth [generation] of them that hate me;"

We see then (what verse 4 above is speaking of). These children can repent and come to God on their own, however. The mother generally has a great deal to do with the moral character of her children. She has not taught them correctly in this particular instance.

Sometimes, the mother could be speaking of the church in our case. In that case, a church which does not teach truth could cause the members to fail.

The third threat involved the rejection of the wife’s children. The reason was that they were children of adultery. This may mean they were products of their mother’s illicit relationships, though probably it simply indicates they were covered with shame by reason of their association with such a mother (cf. Hos. 2:5 and Hos. 1:2). At any rate, the Lord announced they would not receive His love (rāḥam; cf. Hos. 1:6-8; 2:1), implying they would be disowned and become orphans. In this way any reminder of the relationship with their mother would be eliminated.

The harsh punishment threatened in Hos. 2:3-4 seems to imply complete termination of the marriage. The wayward wife would be executed and her children disowned. However, the context clearly demonstrates that this would not occur. This same anomaly occurs in Eze. 16:1-63 where Israel is executed as an adulteress (Eze. 16:35-42) only to be eventually restored to favor (Eze. 16:59-63). Apparently the harsh language was intended to emphasize the severity of the punishment without implying the absolute termination of the Lord’s relationship with Israel, a remnant will survive.