"Back in the day" the BASIC language made sense, as it was right at your prompt in text based interfaces. The same situation today is the web browser, and the ability to open up the developer's console and getting direct access to a web site's JavaScript, html & CSS. Forget BASIC, and introduce your kids to web developing. They will "get it" much faster than "boring dumb BASIC, can't do web stuff, it sucks."
edit: Second the suggestion of Python below, even if it's just for a few months to learn the basics of coding in general. Pivoting a few months in to a new environment is also hard in and of itself, but that's the path I'd go. As a little bonus, then you don't get too stuck in one way of thinking :)