Serious question: You don't speak English primarily at home? I figured most dual-citizen families would speak "the native tongue" in-home, but the "formal language" out of the house?
I have several friends who have done that; my NZ friend in Tokyo has raised his kids that way, but also enrolled them in an English language daycare in their earliest times; they benefited from constant immersion. Another second-generation Japanese/American friend in Chicago was resentful that his parents insisted on Japanese at home. Now as an adult, he's grateful that they were strict that way, but he loathed them at the time.
I took the "easy way out" and learned Japanese mainly to keep up with my children, rather than forcing them to learn my language. It ended up helping in the workplace as well, of course. Over a decade in a Japanese office, it was useful to speak the language.
My kids have learned English in school the same way we all learned Spanish or French in school: resentfully and without enthusiasm. My Japanese is good enough that they don't feel hampered in communication with me. They don't see the need for it until they're around my USA family. I can see it "click" in their heads --
Oh, got it. Here's where it would be useful. But that's only a couple weeks out of the year.