Your question this morning made me want to find this thread and read it!
I definitely agree with you. I think your cousin is going a bit overboard. That being said, I TOTALLY see why it hurts her when her child is excluded from playing with other kids. Being a mom is like wearing your heart on your sleeve, and so it makes sense she doesn't want her child to be hurt.
But those kids aren't bullies at all. If anything, they are being disrespectful and rude. But a bully is someone who is actually trying to bully a person. I could see it being viewed as bully behavior IF there was other behavior to go along with it, such as name calling or getting dominating and up in the child's face, etc. But just telling a child they don't want them to play is not being a bully.
I have very rarely seen my kids tell another kid that they can't play with them, and if I see it, and if they were rude, I immediately jump on that. I don't yell at them or anything, but I talk with them positively and do the "You know how it feels when you want to play with someone and they don't want to play with you? That's how you are making this little person feel." And usually that's enough for them to fix the situation. I can literally only think of one time and that's it. (not including times between themselves!) Usually they are inviting new people over to play with them - it makes me so happy!
At the same time, I don't want them to feel like they HAVE to play with every kid. Sometimes it would be nice to just play with their best friend, or whoever. In those cases, I think teaching them a respectful, friendly way to tell a child no would be appropriate (though if telling them no means the kid is left alone with no one to play with...I would encourage them to play!).
If someone doesn't want to play with my child, I will go and happily encourage my child to go play in another super fun part of the of the playground. Or, if my child wants to play in the same area, I will stand close by and make sure the kids don't try to banish my child away. The playground is open for everyone, and I won't allow them to prevent my child from playing. But I will not try to force them to play with my kid. And, when dealing with kids, I think it's best to approach it positively and encouraging as much as possible. I wouldn't be mean to the kids that didn't want to play with my kids. I might say "Oh, you're missing out on a lot of fun! My child is so fun to play with!" Or something.
Anyway, long answer...but yes, your cousin is taking it a bit far. Instead of teaching her child about the (sad) reality of life that not everyone is nice, she is trying to literally force kids to play with her kids. Not realistic in my opinion. Though, I do think kids should always be respectful and polite no matter what they choose to do. And, I think as parents, it's our job to teach that to them.
I'll stop rambling now.