I think it might be nice to give the teenager a couple of weekends to herself, but I don't think it should happen every time.
First, it sounds like you need to work every other weekend, so that alone could be the dealbreaker.
Second, ultimately, the girls need to learn to live with each other and respect each other. Everyone fights with their siblings and gets frustrated, but most don't have the option to never be around each other. Teach the teenager some coping skills for dealing with annoying, but typical, four year old behavior. Teach the four year old to respect her sister and her sister's things. Kids do not have to share everything - if something is truly your teenager's, don't let the little one use it.
Do they share a room? Can the teenager put a lock on her door to keep the younger one out? My friend is 10 years older than her sister. In high school, she put a lock on the outside of her door so her sister couldn't go in while she was at school or out of the house (but, by putting it on the outside, the older one couldn't lock herself in her room when she is there). It was just a sliding lock, no key, so the parents always had access to her room.
Finally, you're admitting that the four year old gets away with a lot. Now that you know it's an issue, you need to address it and deal with it. Maybe the four year old needs a little more discipline or consequences when she gets into her sister's stuff. Stop letting her get away with things that are upsetting the teenager.