Setting: Modern day, American suburbia.
Googled: Children with fluency in two languages, children who learn English as a second language, children who learn two languages at the same time. (Looking back on it now, this was probably another case of google!fail)
Alright so the character is a normal teenager, he goes to school, argues with his little sister, has friends, all in all nothing really too that special. His parents and grandmother are immigrants from Croatia, having moved to America sometime in between the beginnings of the Croatian War of Independence, around 1989, and his birth, December of '91.
Both his mother and his father are fluent in English, with distinct accents of course. His grandmother on the other hand knows very little English and thus to accommodate her the family mostly speaks Croatian at home and will only use English when the need arises, such as answering to phone or door, around company, etc.
Out side of the home however he speaks English when he's in school and with friends.
My question is though, would the character have learned Croatian first and then English, learned the two languages hand in hand or is there some other method? Either way would he have some sort of accent when speaking English? None of my friends are really fluent in more than just English so none of us could really find an answer ourselves.
ETA: Man defiantly more replies then what I was expecting. Anyhow thanks to all for the help, I wish I could reply to all of your comments but...damn I don't think I'd have the time or the words to express my gratitude. Thanks once again!