Re: Can full communion with the Church occur after 3 divorces if no future marriage will ever occur?
Congratulations on becoming a Catholic, welcome to the family!
As for your question: the advocate is incorrect. The path that the advocate is advising would only be necessary if your mother sought to continue in her 3rd marriage or to enter into a 4th marriage. As far as the Church is concerned your mother is still considered married to her first husband (if he's still alive).
If your mother is not currently involved in a relationship outside of that first marriage then there is no reason that I can think of as to why she would need to apply for any annulments. It might be helpful for her in the future should she change her mind about not getting married again, but its not necessary at this time.
A good confession is all that is required based on the information provided.