As a parent who had a very similar experience growing up, I've tried putting BASIC in front of my young kids. It didn't work at all; the magic just isn't there anymore. If you've got an iPad, there's unfortunately no wonder in "I can make the computer do whatever I want". Also, kids know how modern computers are supposed to look and feel, and BASIC won't get them there.
Sorry.
That's a shame, I'm quite a bit younger than both of you and this is exactly how I learned to program. When I was a kid, computers were icons and a mouse, with no indication of how they worked or how you would go about making them do whatever you want. But I found a bunch of old BASIC books in my school library; the kind of computer in there had no icons, but very much encouraged you to program it. It took me a while to find one of those computers (but not as hard as it is now, they were literal trash back then), but I was hooked once I did.
Modern tech has a huge barrier to entry if you know nothing about it. I didn't even know what "install a program" was at the time, before soon learning it means "get in trouble" for messing up the (one) family computer.
That sounds more like an opportunity to rethink how a new beginner language for modern computers should look like
(Maybe something more like Hypercard I guess - or something that renders to HTML)
That's why they made Scratch, which seems to have been fairly successful
Visual programming is not for everyone. I have two kids, one loves Scratch, the other despises it.
Fun fact, Scratch wasn't the first iteration of visual programming, and one could argue that Lego NXT was even more successful. https://www.nxtprograms.com/help/learn.html