Hi, I'd like to help you with your question.
Sometimes there are things that go on in a family to cause dysfunction. And when that occurs, the children in the family can bond together and find a way to express blame onto someone. In your family, the person who they blame appears to be you.
You cannot directly change how they feel by what you say. But you can work on this problem slowly with a different approach.
1. Back off for a while. Try not to call them or contact them in any way. If you need help with your illness, see if you can ask a neighbor or friend to assist you until you feel better. This will give your kids time to redirect their focus from you.
2. Start counseling. It would be ideal if your kids would go with you, but if not, go yourself. You need to talk to someone about how you feel and find ways to cope better with how your kids react to you.
3. Start being more self sufficient. Don't ask the kids for help. They may be overwhelmed with their own lives right now, and if they are angry at you the last thing they want to do is help you.
4. Start giving yourself to them. Pick the child that seems to have the least amount of anger towards you and invite them to lunch. Offer to pay for it. Talk about their lives and ask about how they are. Don't bring up your illness or other troubles. If you focus on them, they may start to feel less angry. It is hard to be mad at someone who is trying to please you.
5. Keep working slowly to gain their trust. Send little cards just saying hi and I hope your day is going well. Do this once a month or so. Offer to host a dinner and invite them, but with no pressure to attend. If they do come to dinner, talk about them and general topics. If they ask about you, make your answer something light, like" I've been so busy with my job. It's been great!"
If you start slowly, you may be able to break down the walls. If you can get through, then it is time to ask them to go to therapy with you. You need someone neutral who can help all of you reach each other and develop your relationships.
I hope this helps you,