@jburatti
If you and your wife agree to file jointly, she can amend her tax return to MFJ no matter what filing status she used originally. On the amended return she adds you as the spouse, adds your income and other information, and adds the third child as a dependent. You do not file a tax return of your own. You just ignore the extension that you filed. (If you made a payment with the extension, you include that on the joint amended return).
You will probably get a larger total refund for the two of you by filing MFJ.
But she should not file an amended return until the processing of her original return has been completed and she has received the refund.
