Is it permissible for the neighbor to request the return of the item and a refund after I paid her debt to my uncle, claiming that she found a lower price elsewhere, knowing that she did not adhere to the initial payment due date?

What you did is considered fulfilling the right on behalf of your neighbor to your uncle. Since you paid on her behalf, she owes you the amount you paid, and you have a claim for that amount against her. According to the madhhabs of Ahmad ibn Hanbal and Malik, it is permissible for someone who fulfills an obligation on behalf of another, and who was not acting gratuitously, to claim reimbursement for what they paid, even if the payment was made without prior permission. Thus, a set-off occurs between the two debts. It is mentioned in this regard that set-off occurs simply by the establishment of the two debts and does not depend on consent if the two debts are of the same kind, type, description, and are due. By this, your liability is cleared from your neighbor's right in exchange for what you paid on her behalf. If your uncle accepts the annulment, he pays your neighbor the two hundred (dirhams/dinars) that she paid him. If both parties do not agree to what has been mentioned, they can resort to court to resolve the dispute.