J.S.
Stop with the ultimatums and start talking to her... remind her that you have to GIVE respect to GET respect and that you can discuss the house rules together if she feels like they're unfair, but that she has to abide by any decisions you make until she is out on her own. Speak calmly and show your sadness/disappointment, and she just might pay attention.
You should also talk with the boyfriends mother and devise a plan together before you do anything drastic. If she's already threatened to move in with him then both of these kids are playing you, and you and his mother need a united front. Is she even aware that your daughter is suggesting she move in? See if his mother can agree that if your daughter goes to live with the boyfriend, she has to pay rent, pay for her share of food and utilities, do her own laundry, follow the house rules, etc.
As for leverage, I would be careful how hard you push or she might run away, but you should at least have a conversation with her outlining all the things she "gets" by staying at home and following the rules. Explain that if she wants to live like an adult making her own rules, you'll start charging her for all the things she takes for granted. Do you pay for her cell phone, the internet connection, cable tv, food. You can start charging for laundry and housecleaning. Did you buy her car? You could take it away until she's being respectful of your rules.
And lastly, be certain that she gets on some form of birth control. There are plenty of statistics out there about the problems resulting from teen and unplanned pregnancies: http://www.thenationalcampaign.org/ Talk with her about her own hopes for the future and what she hopes for own children someday, then show her the consequences of unplanned pregnancy: such as nearly 80% of fathers do not marry the mothers, two thirds of families begun by an unmarried mother are poor, etc.
Chances are things may get worse before they get better, but if you maintain communication, tell her you love her no matter what, and keep respecting one another, hopefully you'll navigate this difficult time together.
Best wishes!