Eleanor, Sorry not to have replied sooner. I believe that it is dangerous to assume the salvation of all believers' children. I believe that we must be faithful in training our children up in the faith. That is our responsibility. Also we must leave the heart work to God, if they will be saved. My disagreement with those who believe in PR or BR is the idea of "treating children as Christians" before any evidence exists, and before any profession of faith, presuming them regenerate even before baptism without Scriptural warrant. The ideas of Baptismal Regeneration and Presumptive Regeneration are very similar and have the same dangers.
You might want to go over to the Puritan Board and read some threads from their Covenant theology forum. They are totally against Baptismal Regeneration, but are for Presumptive Regeneration. It doesn't exactly make sense to me! They have been discussing this issue constantly. http://www.puritanboard.com/forum/index.php
Consider also this quote by Hoeksema.
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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.)
And this by J. C. Ryle:
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Men sometimes say that it makes no difference whether we think all baptized persons are regenerate or not. They tell us it all comes to the same thing in the long run. I cannot say so. To my humble apprehension it seems to make an immense difference. If I tell a man that he has grace in his heart, and only needs to "stir up a gift" already within him, it is one thing. If I tell him that he is dead in sins, and must be "born again", it is quite another. The moral effect of the two messages must, on the very face of it, be widely different. The one, I contend, is calculated by God's blessing to awaken the sinner. The other, I contend, is calculated to lull him to sleep. The one, I contend, is likely to feed sloth, check self examination, and encourage an easy self-satisfied state of soul: he has got some grace within him whenever he likes to use it, --why should he be in a hurry, why be afraid? --The other, I maintain, is likely to rouse convictions, drive him to self-inquiry, and frighten him out of his dangerous security: he has nothing to rest upon, --he must find a refuge and remedy, he is lost and perishing, --what must he do to be saved?...J. C. Ryle from Knots Untied
Also Eleanor, we all have failed as parents in some ways. God was the perfect parent and Adam fell. The Lord doesn't save anyone because their parents were "good enough" to deserve it. We all deserve hell and only because of God's grace is anyone saved. The Lord is merciful and since he has shown us mercy, we can hope that he will be pleased to show our children mercy as well. We must be faithful to pray and after we have done all we can, we must leave it in the Lord's hands. He will do what is right.