Wes said:
Let me simply say that our differences stem from our view of the covenant and baptism.
I can assure you that this teaching that God's Covenant can be broken is what is at issue here, not our paedo/credo differences.You said that the Covenant of Grace can be broken and that unbelievers can actually be in this Covenant. Ishmael is a clear example that this is not so.

Was Abraham's son Ishmael in the Abrahamic Covenant? No, but he was given an outward sign along with every other male in his household, yet these verses clearly show he was not "in the covenant"! If a person was not circumcised in their heart, even if they were circumcised outwardly, they were not considered "in God's covenant" even though they lived among God's people, because they did not have faith.

The Jews were told to circumcise all their children though. All who are baptized are not Christians, but only those who have regenerated hearts. The unbelievers can have no part in or a relationship to Christ because they are spiritually dead. Ishmael was only given temporal blessings, not eternal ones.

Genesis 17:17 Then Abraham fell on his face and laughed, and said in his heart, "Shall a child be born to a man who is one hundred years old? And shall Sarah, who is ninety years old, bear a child?" 18 And Abraham said to God, "Oh, that Ishmael might live before You!" 19 Then God said: "No, Sarah your wife shall bear you a son, and you shall call his name Isaac; I will establish My covenant with him for an everlasting covenant, and with his descendants after him. 20 And as for Ishmael, I have heard you. Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly. He shall beget twelve princes, and I will make him a great nation. 21 But My covenant I will establish with Isaac, whom Sarah shall bear to you at this set time next year." 22 Then He finished talking with him, and God went up from Abraham...23 So Abraham took Ishmael his son, all who were born in his house and all who were bought with his money, every male among the men of Abraham's house, and circumcised the flesh of their foreskins that very same day, as God had said to him. 24 Abraham was ninety-nine years old when he was circumcised in the flesh of his foreskin. 25 And Ishmael his son was thirteen years old when he was circumcised in the flesh of his foreskin. 26 That very same day Abraham was circumcised, and his son Ishmael; 27 and all the men of his house, born in the house or bought with money from a foreigner, were circumcised with him.

Galatians 4:22 For it is written that Abraham had two sons: the one by a bondwoman, the other by a freewoman. 23 But he who was of the bondwoman was born according to the flesh, and he of the freewoman through promise, 24 which things are symbolic. For these are the two covenants: the one from Mount Sinai which gives birth to bondage, which is Hagar-- 25 for this Hagar is Mount Sinai in Arabia, and corresponds to Jerusalem which now is, and is in bondage with her children-- 26 but the Jerusalem above is free, which is the mother of us all. 27 For it is written: "Rejoice, O barren, You who do not bear! Break forth and shout, You who are not in labor! For the desolate has many more children Than she who has a husband." 28 Now we, brethren, as Isaac was, are children of promise. 29 But, as he who was born according to the flesh then persecuted him who was born according to the Spirit, even so it is now. 30 Nevertheless what does the Scripture say? "Cast out the bondwoman and her son, for the son of the bondwoman shall not be heir with the son of the freewoman." 31 So then, brethren, we are not children of the bondwoman but of the free.

Also this quote from Hoeksema shows about the two kinds of children believers have.

By reason of the fact that the Lord establishes His covenant in the line of successive generations, believers will confess in gratitude before the Lord that He counts them worthy to bring forth the true seed of the covenant. This seed of the covenant, however, does not consist of all children who are born of them, but only of the children of the promise. Certain it is that believers also bring forth another seed. Now, on this side of death and the grave fleshly ties may draw us, so that we say that we wish to see all our children saved, and do not wish that our own flesh and blood goes lost. But, in the final analysis, also in this respect the righteous must live out of their faith, not from their flesh.
(Herman Hoeksema: Believers and Their Seed, Reformed Free Publishing Association, Grand Rapids, 1971, pp. 157-158.)