I really loved this description of your friend @sweetpeaorchestra . Some people seem gifted with a rare ability to delicately balance expressions of sympathy with healthy, matter-of-fact normality, to show genuine care and insight without centring themselves. Often it can come from unexpected places.
When my DC was at their very worst, some of my best sources of support were people who I wasn't previously close to, but who just seemed to "get it". Whereas communication with some of my closest friends and family just became unbearable.
I know people are trying to be kind but personally I couldn't stand the wall meaning "I know how tough things are, I'm here if you need me" messages. They gave me the absolute rage in a way that is difficult to explain, I could almost see their pained, sympathetic head tilt as they typed it out, and then went back to their happy, normal lives, satisfied that they had done their duty by me while being extremely thankful that they weren't me.
Obviously that is just my very personal experience, and other PPs have said that they found comfort in their friends checking in. But I really wouldn't try to do more unless your relative taking the lead. The fact that you even contemplated for a nanosecond inviting your relative to an event celebrating someone else's healthy child makes me think that you don't instinctively get it., and probably are not going to be someone she turns to. I know that sounds very harsh but the vast majority of people don't get it either. It is a uniquely awful journey.