I am glad to see you’re now considering searching your dd’s room. This really is the right decision for her own protection. However, as her dad, I think you should be telling her that’s what you’re doing rather than asking. I would be clear you trust her implicitly and this is what you both need to do to get things to calm down. This is big, scary stuff right now and she still needs a lot of guidance. You’re jumping an age stage imo and acting more like she’s about 14/15 whereas she’s only 11 and from my experience of 11 year old girls (my dd is 14), they make terrible decisions and do the most stupid things at this age due to hormonal changes and brain rewiring. Real headless chicken stuff.
As for lies and the truth, my dd is a truthful person. However, 11 really was the age, where I found dd and her friends to be very black and white about everything and lack the ability to see things from each other’s view points. This caused all manner of arguments between her and her friends. When I asked what had happened to try to help them resolve arguments, I’d get very different versions of events, missing out anything they’d done wrong but be very clear about what the other had said / done. This isn’t because they were lying, they truly didn’t have the ability to see things another way.
As the stepdaughter is about 12, she is pretty much at this stage as well. Your ex should also be considering the possibility she’s taken the switch to her mum’s or lied about breaking it or is hiding it to get your dd punished. If it’s at her mum’s, she may even have forgotten it’s there. But now that she’s said your dd has taken it and everyone is being so hard line, even if she found it, she probably wouldn’t own up.
All round, whatever has happened, it is now easier for the kids to lie, especially as the adults have become so entrenched. All of this doesn’t even mean anyone is a bad kid. This situation is going to replay and even if this time, your dd is telling the truth, there will possibly be times in the future, where she will not be, especially if you and her mum don’t get a handle on things. Or perhaps she will just be economical with the truth as just explained. If one of the girls is lying now, even if it is the SD, she won’t have the cognitive ability to realise the gravity of her actions. So it’s also very important that her room at her mum’s house is searched.
I can totally see why you’re doing what you’re doing. However, what you’re perhaps not realising right now, unless you have an older child, is that 11 is still a pretty malleable age. Once your dd is through this stage, she’s likely going to go through the next stage, where it’s bloody impossible to reason with them and the back chat is insane, yup dd, I’m looking at you. 😩 If you keep on doing what you’re doing, you and her mum are going to find yourselves in much more of a pickle than you are right now tbh.
Once this is settled, I also think you and her mum should talk about the room situation even if that perhaps means she spends more time at your house. My dd would have struggled to share a room long term with a good friend, let alone someone, not chosen by herself at this age. Emotions are very raw. Empathy at 11 is at an all time low with girls and very slowly returns through the teen years.