There are infant sleep studies that can be done (while the baby is awake or sleeping). a pediatric pulmonologist (lungs, breathing) or neurologist (brain) should be consulted.
Do not give up. Any doctor that says there's a brain malformation but doesn't know what to do and is going to send the baby home is not a good resource, to say the least.
Call any Children's Hospital. Have your son call his insurance company and explain the situation. Keep calling until someone will evaluate the baby.
And immediately, have your son and the baby's mother start keeping a daily journal. Keep one page per day in a notebook, and write down nap times, any apnea or seizure episodes, and what was happening at the time (had the baby just eaten, where was the baby, what sounds or tv or lights were on, and the exact time of day and length of the episode). A specialist will need this.
Get all the medical records from the hospitalizations. Request doctor's notes, test results, medications given, etc.
Start filing records very logically and orderly.