Red Chief definitely does not want to go home. Sam asks him that specific question shortly after he and Bill have kidnapped the boy. Here is the pertinent dialogue between Sam and the boy (who decides to call Sam "Snake-eye"):
'Red Chief,' says I to the kid, 'would you like to go home?'
'Aw, what for?' says he. 'I don't have any fun at home. I hate to go to school. I like to camp out. You won't take me back home again, Snake-eye, will you?'
'Not right away,' says I. 'We'll stay here in the cave a while.'
'All right!' says he. 'That'll be fine. I never had such fun in all my life.'
Johnny Dorset, who likes to pretend to be an Indian chief, prefers living in the outdoors like a real Indian. This makes it understandable that he would enjoy the hideout where Sam and Bill are holding him. They sleep in the open and cook over a campfire. There are wild animals around them. As a matter of fact, the outdoor setting adds to Red Chief's fantasy that he is a real Indian, and he becomes more and more savage as time goes by. The two inexperienced kidnappers, and equally inexperienced babysitters, find it harder and harder to cope with this wild boy. He knows a lot of tricks they never heard of before. He is really dangerous, especially because they never know what he might do while they are trying to sleep.