What a nightmare. I haven't had any bad experiences with AA people--I've found it easy enough to avoid the preachy types--but yours is not the first story I've heard of someone being given the "spirituality or death" routine.
For me, what most people call "spirituality" involves things I experience as complete mysteries, and I have no desire to stake my sobriety on a complete mystery.
Sobriety, again just for me, is about believing that life is worth living and experiencing with clear mind, and it involves just taking care of business--being with other people, showing up for work, that kind of thing. If someone really wants to call that a "form of spirituality," that's fine with me.
You might want to check out LifeRing, or SMART, or any of the other secular programs available (see the top of this forum). That way you can say to your parents, and more importantly to yourself, that you *are* working on a program of recovery. Or just work on your own, but keep checking in here if that helps.
Best of luck.