She's being manipulative and self-righteous. "Jehovah's rules" and all that blah-blah weren't hugely important to her when she was having premarital sex with you, or when she was throwing her "husband and spiritual head" under the bus. You're right, it's not at all about Avatar being a good movie or not, it's about the principle of the thing - she knew what she was getting when she married you and she has no right now to go all psycho asking you to change who you are and give up everything that you enjoy.
Every time you backpedal when she pulls a stunt like this, it tells her it's OK to treat you this way. She's counting on breaking your spirit with her threats so that you'll eventually cave and become (or at least pretend to become) the person she wants in order to keep the peace. I'm not saying "be the man/head of the household and tell her that as her head, your final word goes", because I believe that marriage partnerships should be equal, not a headship arrangement like the WT puts out there. But DO stand up for YOURSELF, because the way things are now, it's NOT an equal partnership, and it's not ever likely to be.
In my opinion, if she threatens that she "doesn't want to be under your headship anymore", then you should call her on it. Don't try to convince her otherwise, just say "fine" and start packing your stuff, and then FOLLOW THROUGH WITH IT. I doubt it'll be what she's expecting, and then SHE'LL probably be the one to backpedal and try to draw you back into the drama, but don't do it. Know when to walk away. She and her baby can mooch off of the JWs (and they will, until she finds the "perfect JW" sucker that she's looking for). You, on the other hand, can go to fantabulous therapy or something and eventually move on with your life and be happy and find someone sane and rational without all the cult/brainwashing baggage. You can't save someone who doesn't want your help.