Dear Pooped,
Others will be along with more expertise than I on your daughter's particular problem, but I just wanted to welcome you here and offer my sympathy. My own daughter has gastro- problems -- not encopresis but debilitating in their own way, so I do understand the frustration, as diagnoses seem very hard to come by in this area. Has you daughter's pediatrician offered an opinion? Have you been to a GI doctor with her? My advice would be to explore physical diagnoses and make sure you rule those out before going exclusively the psychiatric route. That said, going the psychiatric route is essential, as clearly what she's doing with her poop is very disturbed. The question is which comes first, the physical problem or the psychological problem? If she can't physically control her defecation, maybe it's driving her crazy. Or maybe she has a developmental disorder or mental illness that's causing her to withhold and then act out as she does. She needs a thorough medical work-up. As long as DCF is involved, can they help you to get her that? You sound like a good person, but that doesn't mean you can figure this out on your own. I would hope DCF could be an ally, not an antagonist.
Above all, though, I think you need to protect your toddler. Violence toward the toddler is unacceptable. If I had a child in the home who was being abused I would be looking to get the abuser out of the home. That doesn't mean you don't love your daughter, just that you need to perform triage. Residential treatment for your daughter may be the best option right now. Others here can opine more knowledgeably on that.
Good luck, Pooped. You're kind of used to it by now, so let me tell you from the outside: this is genuinely an absurdly difficult spot you find yourself in. But you will get lots of help here. And I hope you can be kind to yourself.
Sincerely, Rannveig