Cookie,
I understand your pain on the betrayal from both ends. It's hard when dealing with kids specially teenagers... I personally don't have any teenagers at least not yet ( yr old) ... but I know 1st hand how hard teenagers are to deal with as I was one myself and my parents had a hard time with me.
Although its not an easy thing to experience, my ex-best friend (another story for another day) has 1 teenage son and 1 18 yr old. She's raised them with her new husband since the youngest was in diapers.
Her youngest (I think he's about 15 or 16) decided 2 summers ago to go live with his dad in Vegas. She even had a nervous breakdown b/c of this. Odd thing is that she let him go thinking he'll realize what he has here vs what he'll have out there. Although he's a good kid, he has a mouth on him and she'd been having trouble with him for sometime. So he left, summer went by, fall, winter, spring, and soon she started realizing that he was somewhat ok (looking past the mom dad did this and that to me... b/c he didn't like rules or chores which he has to do in Vegas and not with her). At 1st she'd always ask him so when will you be ready to come home. As time passed she realized that he needed to explore his dads life and be more involved (more than just the occassional child support payments he gave).
The odd thing is that for 13 years, she & her new husband had been trying to have a baby (1st biological child for him) but couldn't keep a pregnancy going. She mis-carried a couple times, and eventually she became discouraged and last year she convinced him to give up on trying and she was going to get her tubes tied. Well they went to the Dr. for the prep for that procedure and they found out that she needed to be treated for something in her pelvic area. She was treated and had to wait at least 6 months before she could go ahead with the tube tying. They waited and about 2 months into the 6, she found out she was pregnant.
Since she found out she was pregnant, she stopped asking Jesse (youngest) when he was coming home. She changed it to, if you need somewhere to go you will always have your home here with us.
Do note that they do get weekend visits about 2-3 times a month for Jesse to come home and visit.
On the other side of what you're experiencing is that your 16 year old has somewhere she could turn to instead of being a run away or go to someone who would take advantage of you.
Believe me I understand that you would prefer her to be with you but at the same time after 16 (+,-) yrs of you being responsible for her, maybe its time for you to take a break and let your husband deal with the teenage problems that come along with having kids.
Even if you feel this way (previous paragraph) this by no means reflects other than you are a good parent.
Also, remember that kids sometimes will change their "move" mind, b/c guess what no matter where you go there will always be rules you need to follow, along with chores, and permissions.
Are you at least in the same city or state as your daughter? You could possible start setting up "mending" sessions with her without her even realizing that is whats on the agenda.
Sometimes we need our own space, that's maybe why I decided to move into college rather than commute back and forth. Something to consider.