I think he was really stupid (which is entirely possible) if he thought placing the purse there with her clothes folded inside would look like she ran away. Yeah, wouldn't she take the clothes with her? And, I never ran away from home, but if I was planning to, I would take a lot more than just one change of clothes. Sierra's mom left before she did and she was home alone, she could have easily packed a larger bag to take if that was the case.
I think either he placed the bag there to throw LE off or he made her get out of the car and remove her clothes and place the clothes in the bag herself as a way to humiliate and to gain control over her. My only issue with the latter though is that this would mean she would be naked in the car which would be risky to drive around with her like that unless he made her get in the trunk or lay in the back seat covered up.
LE retrieved from his trailer a blanket, pillow and his shoes, so Sierra could have been covered with the blanket after her clothes were removed. MOO