The New Age weirdness and the DD weirdness are separate issues, as I'm sure OP knows, but other posters may not. But everyone would agree the DD weirdness is the most serious problem here, so discussing that is surely the priority.
OP must be petrified when she's asked for help and then been bombarded by paedo-gangers and Mumsnet's hi-kickin'-out Leavethebastard chorusline. But, for once OP, everyone is telling you this is a bit more than just a particular way of parenting. Yep, everyone.
Your best-case scenario is you've lost your adult status and any form of normal respect from your family. That's not good and that's serious. Your worst-case option is that DH is either paedo-ing one of the DDs, or about to.
Your burden is added to by the fact that you are the only one who is going to deal with this - in itself a bad sign. That's a huge burden for anyone to carry, too big to carry alone. esp when you've been undermined.
Get help - talk to the NSPCC and see what they say. Move bedrooms for the New Year, getting the whole family to help. Talk to trusted friends (not family). Establish a safe place to go to with the kids in case of emergency, which will make you feel better. Then, and only then, make a time alone with DH to set rules as The Rocks listed above. Explain that the rules will stick and they are non-negotiable. Do not threaten to leave unless you mean it (which at this stage you prob won't.)
Telling someone to be firm is way too easy - being firm is very hard, and you have every sympathy of mine. But it's the only option here, so you need to make it easy on yourself as humanly possible, which means making plans and getting help. Good luck.