sleep problems in 6 year old

Hi!

I have a six year old girl who for the last 3 and half mths is not sleeping well in the night. She is sleeping at an avg of 3-4 hrs. She has difficulty to go to sleep fast and wakes up after 3 hrs and then cannot fall asleep . then , maybesome nights she may fall asleep at 6 am and wakes up at 9 am. This was never a problem before and wld sleep for 11 hrs till June this year. We visited India and she was ok and this cycle of not slaaping has started after coming back form India and is 3 1/2 mths already. She was operated for adenoids last year and gets cold very often . She has a blocked nose but no difficulty in breathing but there are breathing sounds when she is sleeping. When she is not in sleep, she will just lye down and close her eyes and when i ask her if she is waake she says Yes, she is trying to sleep but hrs will pass and she just does not fall asleep.
She feels hot so we put on the fan and aircon before sleeping and then put off the aircon while the room is cool. She recently told us that when i scold her she wants to cry and then she cannot cry as the Dad as an empty threat told her he will leave the house and go and stay with a friend and that has hurt her deeply. Cld it be this that is affecting her sleep. The dad has tried to convince her that it will never happen and was just to threaten her which he apologized to her. But even after that she is still not falling asleep easily and wakes up and lyes down with her eyes closed , cannot sleep and is resulting to dark circles and sleepiness in the afternoon which she cannot sleep as she is out of the house in school in the noon. She is ut of the hse for 7 1/2 hrs and seems that she is still not tired.Pls advise as to what cld be the root cause of this problem as we are also not sleeping as the child is not sleeping. the whole family is distressed. pls help!!Is this to worry or not to worry....??