Hello,
Yes, your wife will have to file the Family Regrouping Application for you to join her in Spain. Once that residence card is issued you will have the right to live and work in Spain as long as her permit is valid. After expirations, you will both have to apply for the renewal.
Please feel free to e-mail me on Patricia at Lawbird.com if you wish to learn more about the documentation required and that we study your particular case.
Best Regards,
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