If I had this fun day planned with my kids so I, as a mother, could spend some quality time with them after they have been at school all week and I was working, I wouldn´t give it away for anything. I'm not a mother, so this is a hypothetical situation. But I don't think I'm far off from what most mothers think about this. It must be really hard to spend so much time away from your little ones, so giving away the one day you get to do something fun for them is not something you easily give. That's why I completely understand u/BigMamaO in this situation. She had a fun date plan, and her brother wanted her to give it away to take care of a kid that's nothing to her? This guy definitely was out of his mind.
Which takes me to my second point: responsibility. If you agree to do something for someone. Then you can't just drop that responsibility for somebody else to deal with. You agree to it, so it's YOUR responsibility. I hate that kind of people. I hope that this woman got to set a boundary with her brother so that this situation doesn't repeat itself.