Rodriguez apparently believed Chavez was having a relationship with his wife.
Chavez, who suffered head injuries, is hospitalized in critical condition.
An Amber Alert was issued for the son, but both mother and son were later found safe at a relative's house in Fontana. The woman says she learned about the Amber Alert through the television news and called police.
Police say they found Rodriguez' 1999 Ford Expedition on Sunday abandoned 20 miles east of Pomona in Bloomington. They believe Rodriguez may have fled to Mexico.
Rodriguez is being sought by police for attempted murder. He's described as Hispanic, about 5 feet 8 inches and 170 pounds, with brown hair and brown eyes.
Anyone with information should call the Pomona Police Department at (909) 622-1241.