DD12 is breezing through algebra, so I'm looking for other math for her to work on without getting farther ahead. I'm debating between the AoPS Intro to Number Theory and Intro to Counting and Probability books. DD12 does not like online classes, so I want a book we can work through together. Does anyone have a recommendation for one or the other of the AoPS books, or a suggestion for another book?

They're both good books. I might try counting and probability first. It's useful material and builds up nicely from chapter to chapter.

DD just got into the AoPS stuff and is working through the Intro to Counting and Probability at school (her great teacher this year lets her work on her own; we're going to miss her). DD really loves it; I had looked through the contents of both the books you mention and Counting and Probability looked more different from stuff she already had so we started there, but we are also going to be trying to go sideways rather than pushing ahead so I imagine she will do the Number Theory next. The AoPS books really do seem to explain things in a very engaging way.

After that if she finishes the Alcumus stuff we might look more into either programming or math competition material. AoPS has a programming course but it's at pre-set times and live (and in the evening on the East Coast) so that doesn't work for us now, but maybe there will be more available in a year or so.

Good luck!