You did not take the birth process personally and did not get enraged with your child during labor (well, there were those few moments!!). Understand that this process is similar. As your "baby" goes into labor and is giving birth to her adult life, it can get ugly. A bit like the first time around. And, just like the first time around, you are in charge of know what to do and what not to do. Here's what to do...
During pack up and at move in (or even earlier in the "getting ready" part), they may want to fight over every little thing ("You're not the boss of me!") and of course, they know it all..and I do mean, all. Besides, they are the ones going to college and WHAT can you possibly know about this? Just walk away...take it up later if necessary. Relax, it will be over with soon enough-just like labor and delivery.
Let them have their anxiety, irritability and anger. The kids who "go away mad" seem to make a faster and healthier adjustment to the "pseudo-adult" world of college than those who "go away sad". It's as if they use their anger to launch themselves out of the "womb" of home and family.
If they leave "sad", they may be back because they weren't ready to leave in the first place or there are other issues at play that you might not be aware of or understand yet.
So, pack up the kid and send 'em off. Congratulate yourself on getting this far. You've done all you can to instill your values in them. There's nothing left to teach on the university doorstep. They are experiential beings and oh wow, will they ever make their own mistakes. Better now than when they are 30. They've got a tremendous amount of learning to do and colleges teach more than just coursework. They are "preschool" for adult life.
Leave your college student on as positive terms as you can. You don't want to have to call and apologize later. Not too much mushy stuff. Tell them you have confidence that they've "got this" and go on your way. Leave in such a fashion that they won't worry about your feelings. They will "rent" your emotional state, so be confident even if your knees are shaking. Fake it. Now, go home and enjoy your reward. Soon enough, there will be an entirely different list of things to worry about with your college student.
As you have always done, walk off the edge and know that your wings still work.