She is correct. They only have one mother and the law and courts willl back her up on this. She is their mother and you are their step mother. They can address you as stepmother but not mother. If you file any motion about this you will lose.
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A person has only one mother and one father. A stepparent can be even closer to a child than a biological parent, but the correct title is stepmom, or stepdad. The mother can claim you are trying to commit parental alienation, confuse the children, and eradicate her existence in the child's life. It is highly doubtful any motion you bring will succeed in having the Court order the children to call you Mom, unless you are able to do a stepparent adoption.
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I agree with my colleagues, you can let children express themselves, but DO NOT let them call you "mom", "mother", "mommy", or any variation, except step-mom. You are not their mother. If they file a motion you will lose, and judges do not like this kind of behavior.