I agree with Judy. I'd be worried if your God daughter were having these issues under normal circumstances, but these aren't normal circumstances. Most 4 year olds haven't been through what she's been through in her life.
In the her four years of life she's spent one year in an orphanage where the care has been perhaps questionable at best, experienced some developmental issues (to be expected, given the circumstances), adopted (which is a GOOD thing, I'm not saying otherwise), taken to a new country where she's learned a new language, adjusted to a new culture, new food, a new family, found security, and then has had that security shaken by a divorce, and is now living life in two homes.
With no disrespect intended towards anyone, I'd be a little worried if she WASN'T showing some signs of stress at this point. At least she's not internalizing her stress; instead she is finding ways to soothe herself by carrying her blanket with her everywhere. I would encourage her dad to allow her to keep her blanket with her if it makes her feel more secure; for heavens sake, she's been through enough changes in her life already, and if she's finding comfort in her blanket, then so be it.
I think it's more or less a temporary thing. What she probably needs is more reassurance from mom and dad, not less. Both parents need to spend time with her right now, and if she needs to be held and cuddled, then they need to do that, especially mom. While your God daughter sounds like she's fairly independant, she's still vulnerable for a variety of reasons, and both parents need to make the effort to reassure her that she is loved and that they love her. Regression in behavior during times of stress is common in kids this age, and it needs to be handled with sensitivity by the parents. Busy or not, both parents need to make time for the little girl...she's only 4 and the world is a very confusing place for her right now.
I'm not sure what that child life specialist meant when she said the little girl needed to find her security internally, not externally...my best advice is to encouarge everyone to cut the little one some slack. She's been through a lot in 4 years.
Maybe her parents could talk to her pediatrician...he/she may have some suggestions about how to best support her. Some counseling may be in order for the little one.
Be sure to give her lots of hugs, and be there to support her best you can.