Again, there may be a semantic problem here. Dogma, as I was taught, is revealed truth. Thus, it is found in Sacred Scripture and Sacred Tradition as it is recognized as such by the Church. Doctrine, while being a teaching on faith and morals, is not, by that fact, a dogma. So, all dogma is defined doctrine, but not all defined doctrine is dogma. I don’t think that the Church has dogmatically or infallibly defined that “God is love” (1 John 4:8, 16), but it is an explicit teaching of Sacred Scripture involving faith and morals. The lack of an infallible definition does not suggest or imply any doubt that God is love.
Leaving the semantic question aside, let’s go with your idea (defined doctrine in error) and see where it takes us. If your thesis is correct, it would seem that one should be able to identify a doctrine that the Church has defined, but for which she admits error. The error we are talking about, based on previous posts, was that the Church later repudiates a doctrine she had once defined. I am unaware of that ever happening, but I am open to looking at examples and considering arguments in that regard. Just to be clear, this is not the development of doctrine. A defined doctrine may be incomplete or its definition improved, but that is not an error, per se.
The next thing, so it seems to me, is to consider if a bishop(s) or a pope can assert a teaching on faith and morals that turns out to be in error. I mean to say, can they assert a teaching as bishop, as pope and be wrong? If they are not speaking as a private person, but from their teaching office as bishop or pope, would that not be an exercise of the ordinary Magisterium? Can bishops or popes, then, in their ordinary Magisterium be wrong? My theological opinion is most definitely.
For example, after the tenth century, popes, such as Gregory VII (1073-1085), Innocent III (1198-1216) and Boniface VIII (1294-1303) considered Christ to have given them a fullness of power that was supreme both in and outside of the Church. This led canonists to teach that both spiritual and temporal authority were in the hands of the papacy. The pope merely delegated temporal authority to the state. The most extreme formulation of this notion, however, was Pope Boniface. He asserted that the pope, because of his superior spiritual position, establishes earthly powers and judges them. Even in the temporal sphere, his was not a human, but a divine power, such that whoever resists him (as the Roman pontiff) resists God. This is clearly a teaching concerning faith and morals, it is from the pope qua pope, and it is an error. What is not found here, in my opinion, is the pope (or Ecumenical Council) defining a doctrine of the Church. This, I think, is the answer to the question with which we are dealing here.