AITA for refusing to let a younger sibling come?

My daughter turned 9 at the start of the month. She wanted to have a “paint and sip” party, where basically she and her friends make crafts while they drink “dirty sodas” (soda with creamer or fun non-alcoholic mix ins). I thought it was fun. I agreed she could invite 7 girls, including a close friend of hers “Brittany”. Brittany has been over our house several times. Almost every time, Brittany has shown up with her younger 5 year old sister. I end up entertaining the 5 year old so the girls can play without her in their hair. The mom has never asked if little sister can come, she just shows up. I once mentioned something to mom and she said culturally, it’s normal for them. I made it clear she doesn’t play with the older girls and she was fine with that. I don’t mind entertaining her, so I’ve let it go. But my daughter made it clear she didn’t want the younger sister there. Brittany also mentioned to me once she wished her sister didn’t follow everywhere.
The issue with the party is that I won’t have time to entertain a younger child. Before sending out the invitations, I called Brittany’s mom and explained this invitation was just going to be for Britany. Her mom seemed offended and said her youngest had to come. I said I understood if her family did things differently but this invite was just for Brittany so if she couldn’t come, let me know. Her mom later said Brittany would be there and promised it’d just be Brittany.
Come party time…Brittany’s mom arrives with both girls. Both girls start walking in. I briefly distract the 5 year old and compliment her outfit, I then tell her mom what time the party will be over. Mom is trying to nudge her youngest in. I gently step in front and say warmly “we’ll see you later”. The little girl looks up at me with big eyes and asks “can I play too?” I gently tell her “this is for the big girls. I’m sure you’ll have fun with your mommy! See you later!” and I shut the door.
The party was fun. The girls all slept over. Next morning, Brittany gets picked up by her mom. Once Brittany is in the car, her mom tells me that I was rude and her youngest “cried all night”. I said her youngest had to learn she wasn’t invited to everything and reminded her of our talk. Mom called me heartless and said I don’t understand as I only have one child. I pointed out even if I had another, my children would learn they won’t always get invited.
This mom has trashed me to other moms, some were on my side, others on hers. AITA?
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