ponsettia this is a difficult one.
I don't know the problem and so I can only assume it is bad/difficult behaviour (correct me if I am wrong). If the behaviour is a problem, you really need to get it sorted and get your dd the help she needs.
If you are asking if you should tell the social worker, that is a tough one.
In some ways it is easier to tell once you have got the help and it is worker. At the very start it is harder to see the wood for the trees!
If you tell too much it may look like the problem is bigger than it really is.
If you do not mention it at all it could look like you are hiding something.
Even if the behaviour is unrelated to the adoption or unrelated to school it could cause problems when your new child arrives.
My dd is 9 now and between age 5 and 7 sent went through a very difficult stage. We ad contemplated adopting when she was 5 but did not, for unrelated reasons, and I am now glad we waited. My dd has dyslexia and I think this contributes to her bad behaviour at home but she is well behaved at school. The behaviour lasted about 2 or 3 years.
My dd can still can be difficult! However, I feel I can cope and handle her behaviour and a new child and their behaviour. I had support from the schools link worker and I also attended an excellent parenting course called The Family Links Nurturing course.
www.familylinks.org.uk/
I would say you do need to be honest but you also need to be balanced. Speaking to a social worker right after an incidence of 'bad behaviour' from your dd may make it sound like you can't cope, where as a cup of tea and a bit of space later and you and your dd may be calmer!
I hope you get through this difficult time and work out what is best. Good luck.