Why is your DH sleeping with his 9 year old? That is not normal. Your DH needs to set some boundaries.

As far as disengaging, I take myself out of the situation...go for walks, go out with friends or hang out in my bedroom. If your DH wants to engage her whims all weekend ling, find something to do by yourself and enjoy your weekend.

SD is nine. She'll be hitting puberty soon. I'd ask him if he plans to stop sleeping with her before Children's Services shows up at the door.

I would break it down to DH the things you expect to start happening/stop happening if he wants to keep a happy marriage. Tell him it will eventually hurt your sex life if he sleeps with his nine year old daughter at night instead of his wife. Tell him you are no longer willing to participate in outings and activities with the SD because her behavior bothers you.

Once you have outlined what you will not tolerate any longer simply disengage. Don't cook meals when the SD is around. Don't talk to her at all except for cordial greetings and short responses if she speaks to you. Walk away from situations where you are tempted to say anything to correct her behavior or where you may feel the need to tell your DH that he isn't handling her correctly. Let him (hopefully) get sick and tired of catering to her every whim without help from you.

I go for a nice long run myself when things become tense around here because of SS. I have been losing weight from the amount of miles I'm logging these days LOL and I've been a runner for years so I didn't have any excess weight to lose. That's how often my SS acts like a a$$hole.

Children are supposed to learn to soothe themselves as toddlers. Your SD has been too coddled to go through that normal stage of development. DH is stunting her.

I'd lose interest in sex if I was married to a mini husband.

You asked for suggestions and advice, here we go... but keep in mind I'm a heartless SM bitch who does not tolerate children to decide over my life.

Good for you to stop walking on egg shells !!! Keep it up, take back control and make it clear, only one Alpha female per house and it sure as hell will not be a 9 year old brat.

1. Wants Daddy to sleep with her cause she's scared, laugh and say, No sweety in this house married couple sleep together, leave your door slightly open and you can have a night light, but you are way to old to be calling this excuse... (yes she's manipulating Daddy to get him away from you)
You can ask her straight out, does mummy sleep with you at her house - if it's yes, tell DH to talk to BM, kid needs to sleep in her own bed, if she says no, simply say, well there you go, you are perfectly capable of sleeping on your own.

2. Princess sulking about plans for a day, or meals, or restaurants.... Oh I loved this, my usual statement to the brat... Well pumpkin, the day you are paying for the entertainment will be the day you can decide what we are going to do, when and where, but until that day you have no say - understood? (This I've said more then once in the house as well, when I changed curtains and Aergia got mad, or when she wanted to paint her room and I said no.... the day you contribute financially towards the house hold, might be the day you can say something and until your name is not on the Deed you keep your mouth shut, I will decide)

3. Getting all teary eye cause she's not getting her way and wants to go back to BM - this is where I'm different from you, I will say, fine then go back to BM, come on chop-chop, I have plans for the rest of the evening... I will drop her ass off at BM's in a flash...I'm not begging a snot to stay, and seeing daddy is not parenting he can loose a couple of hours with her.....

See this whole thing is DH being a Disney Dad and not parenting, anything not to hurt my Princess feefees.... bullshit, does not work like that, she needs to learn from a young age, you can't always get what you want, life is a bitch till you meet this SM, deal with life and stop running away, you will always be in situations you don't like, but make the best off it.
You should actual lay down the law with your husband, he should be the one parenting and not you, you can simply ignore her and be all over DH and get him to step up, Yes I've bluntly told SO more then once... why don't you take possession of your own balls or do you like Aergia and BM coddling it? The days SO made life plans with his teen daughter and thought I would simply follow are over, I would do my own thing and tell him, well I'm your partner, not your daughter if you made plans with her enjoy it, no child will decide my life... and when ever SO wanted to get frisky ... after incidents like this, I would simply tell him, eff off go and ask your daughter to help you out seeing she's your partner.... Every time he jumped for BM's demands, I talked about her as his wife, pissed him off, but I would simply say, well we've been together 10 years, yet if I ask something I'm ignored but if your wife snaps her fingers you turn into a flea.... and I did not care if it was in front of his family... it stopped after a couple off times..