Rebecca's father, Harry Cejnar, said today that "nobody in their right mind would do that to their own daughter".
Rebecca (25) grew up in southern California where her parents, Harry and Linda live.
She met Martin McCarthy, a west Cork farmer, on a school exchange trip when she was 16.
Mr McCarthy was 41-years-old at the time and they married three years later.
The body of their three-year-old daughter, Clarissa, was found a short distance from her father's lifeless body yesterday morning.
One theory being investigated by gardai is that Martin McCarthy feared his marriage was about to end and he would have less time with his daughter.
As Linda and Rebecca's sister Jessica prepared to make the long journey to Ireland today, her father Harry said the family cannot understand how the deaths occurred.
"Rebecca couldn't have brought Clarissa back to the United States because Clarissa didn't have a passport.
"The laws in Ireland would mean Martin would have to say that was OK," Mr Cejnar said in a newspaper interview.
"I don't understand it at all – I still can't believe it. Rebecca and Martin were good parents. I hadn't heard of any problems between them at all.
"I just don't understand how this could have happened. Something must have gone wrong. Clarissa was a great kid."
Rebecca took her daughter to see her family in the US last year.
"How could anybody hurt a little girl like that?" Mr Cejnar asked.
"Nobody in their right mind would do that to their own daughter."
"I never met Martin but Rebecca and Clarissa came here last November.
"Rebecca seemed happy. She told me she was. She came back over to take some decorating classes for her bakery and then she went back," Mr Cejnar said.
The grieving grandfather said his daughter and her future husband had an online relationship after she first met him.
"She came home and told me that she was going to get married to Martin. She said she was going to wait until she was 18."
In an interview today, Rebecca's sister Jessica said their family are shaken up following the deaths which they learnt through a "horrible" phone call on Tuesday night.
"Our mam (Linda) and aunt will head over to West Cork now to be with her," she said.
"I don't really know what happened. I am very close with my sister and have visited west Cork a few times. I don't know much about Martin. I know he was older.
"We are all pretty shaken up over this," Jessica said.