This is such a perennial old chestnut on the step boards - but my hackles rise every time I read about yet another poor SM being taken totally for granted by her partner and his ex.
Yes, yes, yes to everyone who agrees this should be discussed and agreed with the stepmum beforehand. And that means, that possibly, she might say no ! As Huge says, the DP and his ex would have to sort something out between them if the OP didn't exist.
But most importantly, even if the OP agreed to this it should be conditional on the fact that whilst in her care she should be allowed to discipline SD properly (what "properly" means is of course subjective and something else OP and her DP should agree on together - but being unable to do anything is plain ridiculous and of course the kid plays up).
If that means she strops off - where have I heard that before - so be it. I'm sick of reading about adults and whole households being held to ransom by manipulative kids - even if that manipulation has been born out of bad parenting. At that stage the DP needs to man up and consider what, exactly, has led to that stage ..... it's certainly not normal ..... and perhaps think about a different approach. Ultimately, a 9 year old shouldn't be able to decide not to come anyway - it's a totally inappropriate level of power to give her - and if she refuses to budge (and her mother doesn't enforce this) then he has the option of a contact order to ensure he keeps seeing his daughter.
And if the DP's concerned that SD is being left alone and/or in the company of an older child who can't be trusted to care for her properly then he needs to inform social services. Otherwise the mother knows that the slightest hint of that happening will scare DP into complying with short notice care - regardless of how practical this actually is.
PS: this is why I thank god there's a huge distance between us and my stepkids (created by ex moving, not us) because I'm sure if we were nearer this kind of crap might have been tried on me too, especially since I work from home which some people imagine means I'm not actually working at all.
PPS: please UC can you clone your DP, and his ex too for that matter, and let us all have copies of them !
PPPS: if my 9 year old was refusing to get dressed they'd not only have their phone confiscated (not that they'd have a phone at that age ?!?) but they'd be dragged out to wherever we were going in their nightwear. That is what your DP should be threatening too - along with a major bollocking for being so rude and disrespectful to you OP. It's outrageous that you're stuck in because of a bloody 9 year old yet your pathetic DP won't do anything about it !