How to let SIL babysit LO when she hates me?

DH met his sis for a night out and they'd been drinking. She was reeling from the fact I'd turned her down for babysitting as it didn't suit me. I'd asked her to babysit but she wasn't available and she offered a different day which didn't suit me. From what DH told me their conversation snowballed into a character assassination of me. DH told me it was very heated and embarrassing in a bar as they were shouting at each other. I'm guessing it was a long time coming and she finally felt comfortable to voice her true feelings. He had my back but the next day all was forgotten between them. I can't forget though. I'm finding it hard to move on from this because yeah, 10 years of pretending to like me must've been very hard for her. I don't know why DH told me all that was said. I know he regrets involving me because he's sick of me mentioning it all. I've showed him all these comments in hopes he has a better understanding of how I feel.

/r/JUSTNOFAMILY Thread Parent