Richard Williams, 19, and 11-year-old Rachel, from Llanfairpwll, in Anglesey, both suffer from sleep apnoea, which means they stop breathing during their sleep.
Rachel has to wear a warning monitor, which alerts her parents when her breathing stops, allowing them to wake her up.
Now the pair are seeking help from a specialist clinic in Columbus, Ohio, after campaigners raised £15,000 to pay for the trip.
Both Richard and Rachel are affected up to 30 times every night, although Richard's condition is different and he is able to wake himself up.
Rachel's condition prevents her from spending the night with friends and says it has affected her school work.
Her brother also finds it has a big impact on his life.
"I have had problems with school and college and I can't go out with my friends as drinking is a big trigger," he said.
Delay
The US trip had to be delayed after a complaint about the fund raising appeal was made to the police.
But an investigation showed that there was nothing amiss.
Mandy Gruffydd, one of the fund raisers, said: "It has been a slow and hard job to raise the money but we've been succsesful.
"People had said that we had deceived them but the investigation from the police showed that they were happy.
"I don't know why someone could be so cruel to a child that is in need of a very importanat operation.
"The complaint has meant that the trip is going ahead later than expected.
"Rachel was due to fly to America in April - by now she should have had the treatment and be starting school."