The arrival of a family member in a senior position is often accompanied by the arrival of jealousy, insecurity, and rumors. The fact that you have a "less than perfect" history with the company provides more fuel for these negative forces.
Hopefully, when you were rehired, all of the employees were informed of your experience, expertise, and education. When any new person is brought into a key leadership position, it is important to let the employees know about this individual's work history. And when the new hire is a family member whose prior term with the company was not a term of endearment, it is essential to bring the employees up to date.
You should not directly address any of the rumors about you. Let your actions speak for you. You can help accelerate the acceptance process by immediately addressing and resolving some high-visibility problems at the workplace.
In addition, spend some time every day meeting and greeting the employees. As they get to know you, they will be more likely to treat you as an adult and act like adults as well.
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