Your are so thoughtful father. My nephew have never spoken in English with native speakers. He didn't studied in English. He is 5 years old. When I met him last month, I was surprised with his English skill. The parents said he likes to watch English vedios and cartoons. I think he accepted the English sound easily because he's only 5 years old. Additionally, he likes to listen and speaks in English. He has a sister, 7 years old. She just doesn't want to hear something in English. when I tried to speak in English with a joke, she disappeared faster than a wind to her room. I think their personality is able to affect the choice of language either. I think you don't need to worry too much. Nice to see a good father :)