Is the apartment rightfully hers, given that she registered it in her name without her husband's permission, knowing that he paid its full price and they have three children?

The apartment is yours as long as you were the one who paid for it. The fact that the contract is in your wife's name does not change the realities of ownership, because what matters are the facts, not official documents if they contradict reality. Therefore, it is not permissible for her to seize it.