@elainer12: First of all, may I extend a welcome to Mayo Clinic Connect. This is a safe place to air your concerns, which to me sounds like two: 1) concerns about G-d's forgiveness and 2) emotional pain you're feeling from your sons.

I share your Jewish faith and can assure you that from an Old Testament perspective, G-d is viewed as merciful, forgiving those who have made errors in judgment - such as mistakes - when they recognize and repent for them. They can do this through prayer and practice in their Jewish faith. Remember that a mistake is different from a malicious act - what you did, hoping for a love and stable family life, is far from malicious and likely a "mistake" many many people make in their lives. There is a vast difference between mistake and sin - the former being an accidental error in judgment, the latter being a knowing violation of a moral or ethical boundary.

You may be able to reassure yourself by reading Exodus 34:6-7: G-d "revealing His character to Moses on Mount Sinai, proclaiming Himself as compassionate, gracious, slow to anger, and abounding in love and faithfulness. He promises to forgive sins and show steadfast love to thousands" . One way to seek atonement is through the practice known as teshuvah: returing to G-d through prayer and acts of charity. Consider attending services at the High Holidays, perhaps donating or creating fundraisers for/to organizations of your choice, volunteering in various ways.

As for the emotional pain you feel from your sons, this does not appear to be something you directly caused; rather it is their personal circumstances. Rabbinal counseling or therapy may assist in coming to grips with those feelings. And going back to volunteering as mentioned above, you may find an outlet for replacing their lack of attention by providing your services to youth at organizations that would benefit from a caring individual such as yourself: a childrens hospital, foster care support, after school activitis, child crisis centers, special needs support centers.

According to Jewish tradition, through the gift of mitzvot - following a holy, meaningful life - you may start to feel the love of G-d in your every day life. You seem to be seeking that, and I feel in my heart you are so deserving of that. Does that speak to you?