Is there any way I can train my Drivatar to overtake a little better?
Not directly. However, what you can do is to teach your Drivatar a variety of entries and exits from corners. In particular, watch the lines of the opponent AI and try and exploit weaknesses by teaching your Drivatar alternate lines to theirs. This may lower your overall Drivatar rating but it may well give better race performance and ultimately this is what you want.