Kathleen - what a wonderful reply.
That is the key, along with prayer - the life you live now, letting the difference in you and the love of God shine out.
Let your life preach without words!
God calls the individual regardless of upbringing and circumstances - 'he knows those who are is'.
My husband was brought up by a bitter anti-God mother and a womanising jailbird dad - he never had any Christian influence at all - yet he walked into a Church on his own!
Looking back over his life he can now see where the hand of God was always there on his life.
Read also 1 Corinthians 7v14 'for the Christian wife (of the unbeliever) brings holiness to her marriage...otherwise your children would not be holy, but now they are holy'
Paul is saying that the wife who stays commited to a marriage with an unbelieving husband brings holiness to the husband, and such holiness extends also to the children who benefit from the holiness of a Christan parent.
At the end of the day, there is no reason or excuse for your children, they've seen you then - and they see you now - but their responsibility is to their personal response to the call of God on their lives.
I have the same battle with my sister and her children, somedays I cannot find the words to pray, and thinking of the lives that my nephews and niece are living now, is just too painful for me to even pray about on times, and all I can muster in my prayers is 'Lord just honour and answer all the prayers and tears of my mam, I cannot carry this burden'
Yet thanks to God - there is a redeemer!
when Job was at his lowest ebb he exclaimed "I know that my redeemer liveth!"
When Naomi had lost everything and returned to Bethlehem with Ruth - There was the Redeemer!
God is in the business of Restoration! He will be reaching out to your children regardless of the life you have lived in the past. Keep persevering in prayer no matter how rough it gets - if they appear to get worse as you pray, that is a good sign because it shows they are fighting the conviction from God - so don't give up!