Do male and female children, who live with their divorced mother and enjoy excellent financial status, share the sustenance they earned through their own efforts with their other siblings, and what is the father's role in this matter?

As long as the children strived to earn their money, and there was no favoritism shown to any of them in the giving, then the father is not obligated to anything. Whoever Allah has provided for is most entitled to their own money, and none of them are obligated to give their brother anything except as a voluntary act. Nor is the father obligated to provide for them as long as they are wealthy.