AITA Best Friend Edition

Backstory: my husband and I have two kids - a 3yo and a 1 month old. I’ve always been an introvert but I had a few years before my kids where I did a lot of going out and socializing with my best friend. Fast forward, we both have our first kid within 9 months of each other. Her and her bd separate and have shared custody. On the days that she doesn’t have her kid, she loves to go out for a couple of hours and socialize and is much more social than I am. All of this is totally fine and I’m happy for her. However, I am the primary caregiver of both of my children and even when I get a break, I like to spend it relaxing in the comfort of my own home. The idea of getting out and socializing stresses me and I know it bums her out because I very rarely go out with her anymore. This past week, my 3yo broke his arm, so we have had to help him do everything. Yesterday I told her that there was a chance I could bring my kids to her house for a bit. A few hours before, I was exhausted due to my newborn not sleeping well and catering to my toddler and I told her we would probably just stay home. This obviously upset her because, to be fair, I am the queen of flaking when it comes to my kids. Am I the asshole for not making enough time for her? And if you’re an introverted mom, how do you prioritize your adult relationships? I’m out here struggling