AoPS is a fabulous way to learn. The explanations are clear and coherent. Everything is derived from first principles and seems to appeal hugely to my mathie's conceptual approach. (And I learned an embarrassingly large amount, even from pre-algebra. Especially about why you do things, not just how.)
I have an undergraduate degree with a science/math emphasis, and I am learning a LOT from AOPS.
In general though, I think a lot of teaching a math-talented kid is moving from the sense that teaching means that you are pouring knowledge into your little receptacle. Instead, you might try to embrace that this is more about facilitating and guiding your learner in his or her own journey. You don't have to be an expert to be a great facilitator. You just have to know when to say, "I don't follow how you did that, can you explain in words?" or "That is a wonderful question and I want to work out the answer together, let's find some resources."
But alternately you can also take a tangent away from the standard school arithmetic -> algebra track, since this is just fun "keep in a math mindset for the summer" work. Patty paper geometry is one I hear a lot about; you can also play with some discrete mathematics like counting (eg.
https://www.amazon.com/Practice-Counting-Competitive-Mathematics-Students/dp/061582630X). If it's new to both of you then you don't have to feel like you're behind!
