ExP and I split up around 18 months ago. Ex mil and I never got on, she's a very domineering person and wants everything her way, she interfered in ex and I relationship and he never stood up to her or defended me which was one of the reasons we split.
ExP and I have a contact arrangement, he visits 3yo dd at my house every Sunday and takes her out for lunch/park etc. I have residence and she doesn't stay at his house, he lives an hour away and I'm not happy for her to be away from her home without me overnight, I'd prefer ex visited her here and he's always been fine with this. At some point in the future this will change of course, but not yet, when she's old enough to benefit then she will 
Anyway, ex mil bought a cot for her and kitted out a room for her at ExP house about a year ago. Then she bombarded me with emails asking why I wasn't allowing overnights 
ExP confirmed he was happy not to have overnights.
I emailed ex mil at the time and told her politely that exp and I have an arrangement with dd. She left me alone after that.
Exp took dd (age 2) to soft play this morning, then gave her back early at lunchtime. Since then dd has been telling me about the peppa bed ex mil has bought her 
apparently she is delivering it to exp, so dd can have it there and sleep in it
ExP mentioned nothing about it when he left. Wwyd? I doubt dd is lying (why would she, she's got good speech and not likely mix up a bed..) I'm not sure whether to ignore it, as mil is overstepping and nothing can be done without my agreement with exp. But I think she's out of order to get dd excited about a Peppa princess bed, aside from anything else dd still co sleeps and when I tried her in a bed dd decided she wanted to sleep in my bed again after 10 mins. Perhaps mil I'd going to try to buy dd fancy stuff that I can't afford forever more though.