Real Estate Law
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No, the mother cannot sign on behalf of the children, and the children can't execute a deed because they're minors.
The only way to get around this is to file a petition in family law court to remove the child's minority to allow them to sign the deed.
The court will appoint a guardian ad litem for the children (lawyer) to make sure doing this is in their best interests, etc.
If you must go this route, I would suggest hiring a local attorney to help you.