I was sorry to hear your husband is giving you a rough time with the kids. You don't need the extra load of guilt from your Christian friend who keeps quoting, "If she divorces her husband and marries another, she commits adultery" (Mark 10:12). You have not committed physical adultery, and if the previous marriage has died marrying another cannot be adultery.
I would prefer to translate "her marriage is adulterated" which is a statement of fact. What Jesus is saying is that in any divorce something which could have been beautiful has gone badly wrong. Both partners and the children have their lives mixed up and adulterated.
Think of a sea captain in the old days of sailing ships. It is never ever right to cause his ship to be wrecked. But a terrible storm might drive it on the rocks. Or his charts could be wrong, or the compass off balance. Pirates could have looted the gold, and cut his mast down. The mate could be drunk on watch, or it could be his own carelessness.
Whatever the cause, the captain admits to the owners that his ship is wrecked and lives have been lost. He may have to begin again at the bottom as a deck hand. But eventually he can hope to captain his own ship again. So with marriage. Jesus said that the wreck of a marriage is always a terrible adulteration. The lives of both partners and the children are adulterated. But that is not the end of the story.
I suggest you talk honestly to God, who loves you infinitely more than you love your own kids. Confess your sin in what went wrong, and the sin of your husband, and the sin of any others who helped to wreck your marriage. Then accept total forgiveness, and boldly look to God for help in picking up the pieces. If you plan to commit yourself to another marriage, I suggest you find a minister who can help you prepare and seek God's blessing in the new relationship.
You might like to read through with your friend, Living Totally: Without Guilt.