You mention that your wife has a new phone. If she was already in the family plan, she won't need to be re-added again. She'll just need to log into her Premium account on her new phone. If she's having troubles with logging in, give her this page which will help her to regain access to her Premium account.
If for some reason your wife has been removed from the family plan, try to issue a new invitation via an incognito browsing session.
Hope that does the trick. Let us know if you have further questions.
Hi Guido, i've managed to solve the problem with Spotify's chat assistance. Since the mail problem was remaining (and loggin in with premium account didnt give any results...) the assistance gave me a direct link to activate the family user in my premium account.