"I would have done that, had I been in his place." This is the proper format (third conditional). Otherwise, "I would do that, if I were in his place." The main difference is that the third conditional re-imagines the past, and the second conditional suggests a possible but very unlikely situation for the present. It is possible to mix the conditional patterns, but your example makes no sense.

Peachey is an excellent teacher, but he is a bit of a strict grammarian. Mixed second/ third conditionals are not often used, but, yes, your example is correct. The mixed second /third conditional shows the theoretical past result of an ongoing condition, a condition that would be true both now and in the past. Let's replace your sentence with an example from real life. If I were in your place......an unlikely scenario -If I were in the place of Bill Gates.....an unlikely scenario I would have done that......the theoretical result in the past -I would have donated a billion dollars to the foundation for the homeless. If I were in the place of Bill Gates, I would have donated a billion dollars to the foundation for the homeless. This sentence makes perfect sense in English. Other examples: If I could speak spanish, I would have gone to school in Spain. (You can't speak spanish now, nor could you then.) If you weren't so naive, you would have realized that he was seeing another woman. (You were naive then and still are now. It is a feature of your personality.)