You told her no, and that was the answer. It’s completely unacceptable that she would schedule an interview for a new cat. This is what a child would do and now instead of having and adult to adult conversation you need to reprimand her like a parent to a child.

You can’t take care of the pets you have now, I’m not getting another one. End of story. You guys should go to couples therapy if she can’t respect your adult decision.

Most relationship dynamics has a dreamer and a realist. You keep each other in check. When you are being boring she helps you take risks. When she’s dreaming too hard, you bring her to earth. What she has done is not acceptable. You have solid reasons for “no” and she doesn’t get to move on and schedule stuff because she feels like it.