Even the holders of 'Covenant Succession' have to admit the obvious reality that not all children of believers are in Christ. So where is 'Covenant Succession' here? Some go as far as to assert that those who do not persevere are not really their true children after all. A scandalous assertion!
If it has to be acknowledged that sadly many children of believers are not in the covenant because they end up dying out of Christ, then where is the reality of 'Covenant Succession'? The reality makes a mockery out of the claim! All the children of believers are not in the Covenant! Therefore they should not be treated as such.
Furthermore, many are in the covenant of grace who were never the physical descendants of Abraham. All the Gentile believers, who have been and are being gathered into Christ, by virtue of that covenant of grace, are evidently not the physical descendants of Abraham. If, as claimed, this covenant is solely the covenant of grace then it has little to do with physical lineage. The Scriptures teach the true children of Abraham are those who have the same faith as Abraham not merely his physical descendants. All believers called Abraham 'father'. He is called the father of the faithful, Romans 4:11: And he received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also. We call Abraham 'father' as we have the same faith as father Abraham.
Only those who are in Christ can truly claim to be Abraham's seed and that in fulfillment of Genesis 17:7. As stated in Galatians 3:28,29: There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise. Physical lineage doesn't come into it!
In fact, Paul elsewhere argues against the claim that physical lineage includes you in the covenant of grace, For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God, Romans 2:28,29.
If physical descent does not guarantee you inclusion in the covenant then it is gross folly to pretend otherwise to our children. It might make you feel good as a parent but it will do nothing for the child.
This text is speaking about a national gathering of the whole nation in which every inhabitant old and young alike will know the Lord and be taught of Him. It has nothing to do with an individual believing parent and their children. In fact, on closer inspection these words are spoken to an unbelieving people. The nation is described as being in 'widowhood' in v4, separated in unbelief from God. Something which can never be said of a believing parent and would be anathema to those who believe in 'Covenant Succession'.
3. Ephesians 6:1-3; Colossians 3:20,24: Children, obey your parents in the Lord: for this is right. Honour thy father and mother; (which is the first commandment with promise;) That it may be well with thee, and thou mayest live long on the earth;
The phrase 'in the Lord' is often employed to again argue for 'Covenant Succession'. However, this phrase is not a reference to the state of children before the Lord but rather is a reference to the terms of their obedience:
 They are to obey 'in the Lord', that is, as far as it is consistent with their duty to God. They must not disobey God in obedience to earthly parents. Our obligation to obey God is prior and superior to any command to obey all others, even our parents.
 They are to obey for the Lord has commanded it. Children are to obey their parents for the Lord's sake. It is dealing with the authority to require obedience.
 It may be a general duty. Children are to obey their parents, especially in those things which relate to the Lord.
To make these words an argument for 'Covenant Succession' is to force the text to teach something that there is no warrant for.