I think to answer that question, TampaBay, is to examine several questions:
1. How is she funded, and would she be able to enjoy her lifestyle (without working) equally well there as in Spain?
2. Is part of her financial funding requisite on her remaining in Spain? I have heard that the Royal family of Spain contributes to her furbishment and upkeep; perhaps there is the agreement between governments that she can agitate for restoration but cannot return to Russia unless specifically invited.
3. Who is Putin and would he permit her to return? She is of no value to him, and he is old-style Soviet, dressed in democratic trappings, after all.
4. What can she possibly offer to the Russian government that would make her attractive to invite back? Her claims are disputed, her imperiousness offensive. If the Russian government thought she was a horse to be backed, arrangements would have been made to un-invite the other Romanovs to the reburial, and glorify her only. That didn't happen.
5. And given the reburial situation, it could be that she just doesn't WANT to go back and lead a private life. Russia is not her home; Spain is. It's her terms or no terms, and Russia isn't exactly saying she's all that and a bag of chips.
That would be my line of questioning and reasoning.