Look, I haven't read all responses, but I'll tell you what I know from my perspective as someone who spends every working day with children in these circumstances: You need help.
It really is fantastic to hear that you appear to be a stable and loving home, and that you really want the best for your child. This is far better than what many kids from backgrounds of abuse and neglect can ever hope to go home to. It's also really positive that she's been placed with you so early in her life. You have a wonderful opportunity to be a positive and healing influence on her.
Here's the thing though...your normal parenting approaches aren't necessarily appropriate here. They will be, in time, but right now they're not going to bring you the results that you want for your step daughter or the rest of your family. If what you've described is the worst of the situation, please count your family lucky. It is very rare to come across children in care who do not have significant behavioural and interpersonal difficulties. It is very normal for teenagers to be wetting/soiling the bed nightly; for siblings to be engaging in sexualised behavior with each other; for children as young as 3 to be physically, emotionally and sexually threatening carers and assaulting them. If refusing to use the toilet and being rude is the worst of the behaviour you're dealing with, things are going well. Please try to remember that this behaviour is in response to the trauma that she's struggling to deal with...it is not an intentional attempt to subvert your family or your values. The last thing this child needs is to feel that she is failing to meet your standards.
I would suggest, in no particular order:
-read up on the effects of trauma on the developing brain. Abuse/neglect changes the way that a brain physically develops. Often children from trauma haven't ever devloped a stable trusting relationship with their primary caregiver. This is fundamental to how our brains develop. This NEEDS to be your priority.
-Speak to the department/her (ex?) social worker etc. Demand that you get support. This is not just about short term behavioural difficulties...this is about setting a child up for life. Tell them flat-out that you want to do what's best, but you need their help. Don't stop fighting for her.
-Relax on the rules/consequences. Look, I get it...I have my own kids and I treat them very differently to the children that I work with. The thing is, that I know my children have a secure attachment to at least one person. I know that, however I respond, they know that they are a permanent and valued part of our family. A 3 year old who has been in care and then placed with another parent/family does not know this. Our approach with kids in care is "therapeutic care". It essentially means that we don't implement consequences unless it's necessary for safety, and we never EVER implement punitive consequences (like denying a treat later in the day due to earlier rudeness). We point out natural consequences and let the child make their own decisions. It's not viable long-term ina family environment, but something more in that vein may be more effective in the short term while you're looking at building relationships and trust. You can always up the discipline as she gets older and feels more secure with her place in your family.
Good luck with everything. It must be a tough situation to deal with, but please PLEASE seek help. You should not have to deal with this alone.