Where can I change the player's X and Z positions when riding a mob?

I know that the Y position is determined by the hitbox values, but is it even possible to change the other directions of the player's position?

I have a mob that is rideable but when clicked, the player sits in the head of the model and clips through. I used blockbench to create the model, is there something there I need to change? or is there a value in the code I can edit, or a line to add to change the player position beyond the Y value? 

I already messed with the hitbox values a bunch and I couldn't seem to get it right. 

Thanks,