Oh dear - not a very professional attitude being shown by the nursery. How very negative of them!
Do you have more details? If it was my DC I'd have chat with DD and try to ascertain if there is anything making her unhappy - is she bored, hungry, thirsty, are the children friendly and sharing etc? 'm not suggesting you bombard her with all those questions obviously but you know what I mean...
Then I'd go back tomorrow and request to speak to her key worker and ask some questions including -
Roughly how many times have they had a stern word with her?
HOw did the nursery deal with it exactly and what did they say to DD?
How did she react to their stern word?
What lead up to her behaving in this way?
Can they see a pattern emerging eg is it only during story time or when she's with a specific child?
When is she happiest?
What activites does she seem to enjoy most?
WHich bits of nursery does she seem to be less keen on?
How much outdoor play is getting on average each session?
Do you have any other strategies for encouraging good behaviour apart from
having a stern word and if so what are they and have those strategies been put in place?
Have a pleasant manner of course but DO NOT be fobbed off. They should be able to deal with this in a much more professional, positive and pro-active manner than they appear to be doing.
You politely hit them with some or all of those questions in a pleasant conversational way and I GUARANTEE they'll be pulling their socks up and trying to think of a better way of handling this behaviour! It points out that actually the onus is on them to be more positive - you're not there FGS. They need to reward her good behaviour and deal more professionally with her not so good behaviour IMO.
Re outdoor play - I'd say you want them to encourage her to have as much of this as possible if she's used to being active.
That post has made me so angry - can you tell?
Good luck 