OP, I apologise for the length of this post and the high-handed tone. Although I'm not a professional, I have worked with insecure children in the past and I feel very strongly that your understanding of this situation is wrong. I realise you didn't invite this input so please forgive the intrusion. I'm saying it because I care about your DD's situation.
You need to see a good family counsellor or psychologist.
I also suggest you speak to DD's teacher/close friends/family members/parents of DD's friends and see if they feel DD is thriving.
You seem to see yourself as a victim, having to put up with a DD and a DP who are giving you hassle. Your posts read as not nearly alarmed enough for your DD's welfare. Perhaps, like DP, you are immature and don't fully grasp your responsibilities to DD. For her sake, stay open to this possibility when you see a family counsellor. You're not unreasonable to want change but you're unreasonable to expect others to change when the responsibility for the outcome (i.e. DD's welfare) is none other than your own. Your proactive behaviour should go a lot further than discontentedly posting on Mumsnet. Your DD is worthy of unconditional love and affirming discipline from people who are either professionals or loving family members. By contrast, your DP sounds insecure, clingy, self-centered and a bit of a whining bully; I wonder how he treats DD when you're absent.
To spur you on a bit, consider this: no matter how close you are to DD now, one day she is likely to look back at her childhood and form her own opinion on how hard you worked to give her a safe, loving environment in which to grow up.
Your DD may be able to manipulate the behaviour in the home (and the only people better at doing this than little girls are insecure little girls) but that doesn't make her responsible for it. She won't be able to appreciate or bear the consequences of her actions, however good she may be at pressing buttons! Please don't let her become one of those unhappy children who compulsively observe every little interaction between caregivers in order to try and get some traction in an unsafe and unpredictable world. Your DD is already coping with inadequate father figures; you need to grow up and make whatever sacrifices are necessary to ensure your child can thrive.
It sounds like you wouldn't have got together with DP if you'd seen poor treatment of DD back then; it should still be unacceptable to you and the buck still stops with you. I sense that a lot of this may be down to tension between you and DP; are you expecting a standard from DD that you haven't achieved yourself?
It's also unrealistic to expect things to be as they were before; the family is an evolving dynamic that has changed forever now, especially since you've had another child. But it could improve again to be something different, new and good. There are great parenting courses and resources available to you and DP, including free parenting lines (fortunately manned by people more qualified and less judgemental than me :) ) Try googling Positive Parenting or Family Lives. There's also a great book called How to talk so your kids will listen and listen how your kids will talk if you're looking for concrete examples of affirming, secure parenting. Available secondhand on Amazon.
At the end of the day, I don't care if DD is swinging from the lightbulbs. I would still consider it your responsibility to place her somewhere safe, sweep up the broken glass, impose an appropriate sanction and take yourself to task for allowing her to get near the lightbulbs in the first place.
Sorry for the length. Good luck.