Asthma is not the first diagnosis that comes to mind, with what you have described. The description suggests the possibility of upper airway obstruction, usually by tonsils and/or adenoids, resulting in respiratory distress, while awake and asleep. The condition, when it occurs primarily while asleep is called obstructive sleep apnea, which is a form of sleep-disordered breathing.
Another possibility, especially if the shaking occurs first, would be some type of seizure activity.
You may wish to discuss these possibilities with your grandson’s doctor but each of the possibilities may require consultation: with a pediatric sleep specialist in the first instance or with a neurologist in the second.
Another, less likely possibility would be cyanotic congenital heart disease. Some varieties of which begin with intermittent cyanosis or turning blue.
And, a final consideration would be breath holding spells as described below:
A cyanotic breath-holding spell is usually predictable and is always provoked by upsetting or scolding an infant. The episode is heralded by a brief, shrill cry followed by forced expiration and apnea. There is rapid onset of generalized cyanosis and a loss of consciousness that may be associated with repeated generalized clonic jerks, opisthotonos, and bradycardia. Results of an interictal electroencephalogram (EEG) are normal. A breath-holding spell can occur repeatedly within a few hours or it can recur sporadically, but it is always stereotyped. Breath-holding spells are rare before 6 mo of age, peak at about 2 yr of age, and abate by 5 yr of age. The management of breath-holding spells concentrates on the support and reassurance of the parents. Some parents feel that whatever the physician recommends, they must splash cold water on the face, turn the child upside down, or initiate mouth-to-mouth resuscitation and even cardiopulmonary resuscitation. A thorough examination followed by an explanation of the mechanism of breath-holding spells is reassuring for most parents. The counseling session should emphasize the need for both parents to be consistent and not reinforce the child's behavior after the child recovers from the spell. This may be accomplished by placing the child safely in bed and by refusing to cuddle, play, or hold the child for a given period of time until recovery is complete.