No she shouldn't ask ex anything. She does presents in her house, he does presents in his house. They are not together anymore.
They've previously sorted it so that they both help their DD get presents for the other, because she's too small to. It's worked fine. Now she should stop doing so, and just not mention it - not communicate at all - as that would be interfering. Right. That's mature.
You have been told twice by your ex to keep your beak out. You are the one not trying to get along here.
No, she hasn't.
First situation: OP explained how they had a fairly friendly relationship with intermittent casual texts. She was fine with that. SO WAS HER EX. He texted too. Then his DP put a stop to it. OP raised it on here as she was concerned that them not being allowed to text as friends would have a negative impact on their DD not being allowed to see her parents get on as friends. OP was generally reassured. But no, having her ex tell her that their MUTUALLY AGREED FRIENDLY RELATIONSHIP needed to cease was not, in any way, being told to 'keep her beak out' Out of what? His own friendship with her that he was just as active a partner in too? Right...
Second thing is this. OP suggests their DD can bring some of her baubles over. HE AGREES THAT WOULD BE NICE. (And it is, isn't it? Nicer than a separated parent saying no, MY house is home, YOU are the NR parent, you're not having any of OUR memories at YOUR house...) Anyway, he then lets her know that DESPITE HIM THINKING IT IS A SHAME, the dd isn't to bring any baubles. 'Keep her nose out'? No, that's really not what he's saying or the tone he's saying it in.
On top of this, OP's been very clear that she has a new partner she's happy with and has moved on. The degree to which posters have basically gaslighted her on this - sneering oh no you haven't moved on, get a life, realise you're not with him any more... it's all disgusting, frankly.
Honestly I have no idea why some threads go this way. Shocked to see one in relationships and not AIBU, I have to say. But not rocket science to see HOW they go this way. A poster comes on, skims the OP, reads a few of the responses before theirs and gets a taste for the prevailing feeding frenzy and dives in.
You lot should be ashamed of yourselves.