It depends on whether there is a provision governing same in your parenting plan. If not, then you should have a conversation with your ex. If the discipline regards some type of punishment that you are uncomfortable with you certainly have reason to object and grounds to do so.
It depends on several factors. First, the type of discipline. If it is physical discipline, then a step parent should most likely not take part in that. However, other than that, it depends on how your ex spouse and the new step parent run their household. There is no "law" that governs this question.
This answer is for general informational purposes only and should not be relied upon for your particular case nor is it intended as legal advice. I have not reviewed your case nor have I met with you and the answer to this question does not in any manner whatsoever establish an attorney/client relationship.
The stepparent has as much latitude as the parents allow. The law doesn't designate how much latitude the stepparent may be given in disciplining stepchildren.
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