Would you invite yourself to a party?

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My son just had a birthday party. He invited a few of his friends and one friend he has in common with his sister, and I'm friends with her mother. This last girl is friends with another girl who is friends with my daughter. She found out where she was going and wanted to come. Her mother allowed this, she came too. Now the thing that gets me is this woman has yet to get my daughter a present for her birthday, even though we gave her daughter one, and she didn't even bring one for my son, not even a card. I didn't say anything to her because I'm friends with her, well I tolerate her for the sake of the kids and our common friend. Frankly I find her loud, and often have to tell her to watch her mouth around the kids. Some of my sons' friends have brothers or sisters, and I plan for this. I didn't have enough treat bags to give her daughter one, invited guests come first. I know she said something to our friend when thay left. She always complains when another kid gets something hers doesn't. Am I over reacting or do you find this to be rude?