You two sound awesomely smart. Chemistry and piano and English and flute and singing? I hope you have kids! They'd be very lucky children.
Tonight, if she doesn't unload the dishwasher, it might make a good introduction into re-splitting chores so that one person doing theirs isn't dependent on the other person. It takes a while to develop a natural flow to a household, so you might discuss that with her, too. That her lack of participation is irritating to you, but you don't want to be irritated and you know that you'll both get into a good groove eventually, so brainstorm together on how to reduce your irritation in the meanwhile. My H and I fought about household duties for at least four years. We ended up resolving it by each of us doing the things we enjoy the most (me: cooking, him: cleaning up after dinner [I still don't get that, but hey, I don't question.
), and the things that mean the most to us (me: decluttering and vacuuming and making the interior welcoming, him: keeping the yard up so the outside looks welcoming). If us two knuckleheads can find a smooth spot in household stuff, I'm sure you will, too.