DP is going to court to get proper access to his DD. Over the past three years ex has allowed him anything between 45 mins to 6 hours a week depending on what she feels like at the time. It currently stands at 2 hours. She tries to justify this by saying DP is an inadequate parent because DD got got mud on her clothes playing in the park or DD had a toilet accident. 
His DD is 3 1/2, her parents splitting when she was 6 months old. She has been repeatedly told daddy chose fifi and her DS instead of you. We don't like fifi and DS, they smell etc. I was not the OW. She was allowed to see us for a month? back last summer and we got on well. Her and DS also 3, not as much but nothing dramatic.
DP and I are expecting a child in July, DD is unaware at present as ex has stated she will tell DD it isn't her brother and will say DP is lying.
DD hasn't been allowed to see any of DPs relatives in the 3 years they've been apart as ex will stop contact. DPs family are normal people. Think nurses and shop workers not junkies and drunks IYSWIM.
With it all going to court DP is requesting a whole day a week where DD can be part of our family and of her extended family without interference. Assuming this is granted, I'm not sure how to approach DSD. It will be a lot to take in with new siblings (DP has taken on DS as his own), grandparents, aunts and uncles. Being away from her mum longer etc. of course being told she hates us could be difficult too!
Should I try to engage her if it's just the four of us, or wait til she approaches me? If she's being naughty should I say something or summon DP to get him to?