Hi, welcome to the forum, She seems to have idiopathic insomnia. It can be associated with stress, anxiety, or circadian rhythm sleep disorders. Quitting smoking is not associated with insomnia. Nicotine craving may be responsible but not for long term.
They may also be associated with sleep disorders (eg, sleep apnea, periodic limb movements), medical conditions that cause pain, psychiatric diseases (eg, anxiety, depression).
The investigations which will help to diagnose the type and cause for insomnia are Polysomnography, Multiple sleep latency test and Actigraphy.
The therapy for this condition includes retaining of normal circadian rhythm by non-pharmacological therapy which includes; Photo therapy, maintenance of sleep hygiene. Psychotherapy can also help him to learn how to cope and deal with the various stressors in his life. A short course of sedatives will help her.
She may go for nicotine gum or transdermal patch which can reduce the craving and may help. Do not worry, follow the above mentioned methods and the symptoms will alleviate. I suggest you to consult sleep specialist or child psychiatrist. Take care and regards.