Right of first refusal means that if the custodial parent is unable to care for the child during his or her normal parenting time, the other parent will be offered the opportunity to care for that child (say mother has to go to hospital or business trip, the father can care for the child before the grandmother or another person on mother's side is asked to care for the child. This is maintained either in a property settlement agreement, or by court order. Check you existing orders to see if this has already been covered in your agreements.
The article below may help.
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If you know she is not available during the time child is at babysitter, then you inform her that you will be taking the child, unless she becomes available. If it is a one-time or I frequent occasion, then she should inform you she is not available and give you the option.
973-984-0800. Please be advised my answers to questions does not constitute legal advice and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.
Agreeing with the previous posts, right of first refusal essentially gives you the right to see your child and spend time with your child ahead of the child going to a babysitter or the like.