God knows your situation, and the most important thing I can tell you is to seek His will for your future. He loves you, and He alone knows what is best for you.
Does this mean you should ignore your children's feelings? Of course not. Undoubtedly, they feel the loss of their mother very much (just as you do), and it is probably very difficult for them to imagine anyone taking her place. At the same time, they probably don't fully appreciate your loneliness. Ask God to help you to sit down and talk honestly with them. You need to understand their concerns—and they need to understand yours.
If God brings across your path someone with whom you can share your remaining years, then rejoice in this and be grateful for His good gift of marriage. At the beginning of the human race, God said, "It is not good for the man to be alone" (Genesis 2:18).
At the same time, remember that marriage always brings adjustments, and this is especially true when two people are older and more set in their ways. Adjustments may also be difficult if you both have children and grandchildren from your previous marriage. These issues shouldn't prevent your remarriage—but they do need to be faced. Above all, ask God to guide you and help you communicate with your children so there will be peace in your family and not resentment or misunderstanding.