I'm a stay-at-home mom; what are some things I can do to engage and further my intellect?

You can read different authors if writing interests you. You can enrol yourself in some online course and add to your skills. Sit and think what you like to the most, what you are passionate about and you can pursue doing that. It is never too late for anything, so don't let anything stop you. I too am a stay at home mom, and it was so difficult to get out of this zone. But recently with the help of my friend's motivation I learned swimming. And learning a new thing boosts your confidence, gives you self-worth. So, all I meant is, try new things, come out of your comfort zone and challenge yourself.