Your rights of visitation and your children's right to see you are not dependent upon child support - although if you do not pay child support and are in jail because of it, your visitation will be seriously curtailed. A biological parent is entitled to visitation in almost all but the most serious situations where visitation could be dangerous to the children's physical and mental health. Even if the bio-parent has made mistakes, has a criminal record and substance abuse problems, supervised visitation can be arranged.
Most people do not have these problems and the visitation can be court ordered at a temporary hearing. You should obtain legal counsel (although people can represent themselves in court) and file an action to obtain visitation.
Whether a divorce is uncontested depends on both parties, who have to agree to the terms of the separation/divorce. It is apparent from your question that you and your wife may not be able to agree on a whole lot since she will not let you see the children.
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