There is no easy way to handle this.
The other parents who come to you about what happened at the birthday party or in the classroom need to be stopped. "I'm sorry, but you need to deal directly with her" (birthday party) or "you need to deal directly with the school" (classroom/recess). "It is not appropriate for me to deal with these issues with your child, as sympathetic as I am."
And while you feel these parents are coming to you for help, by definition, what they are engaging in is gossip. I know people feel that gossip has to have a bad intent, but that's not true. Simply stating things to a 2nd party to lower that person's regard for a 3rd party is technically gossip.
Just because you are in the PTA does not make you responsible for children. Just because you are her friend does not mean you intercede on others' behalf. You deal with yourself and your child ONLY. I know it's flattering that people come to you, as it is flattering that she comes to you, but it really doesn't sound like this is beneficial for you at all. You have to create more boundaries!
You say all the things that you do for her, but you don't say that she's a particularly good friend to you. Does she support you, help you out, listen to your problems? Or does her neediness just feed your ego a little bit and invite more neediness on her part? Try to read into your actions to see if she is taking them the wrong way.
So, don't tell her where you are going. She doesn't have enough sense to refrain from inviting herself and her child to a party where no invitation was extended? You have to keep totally mum about your plans. Just "Sorry, I have plans that day." Period.
You probably should cut back on your get-togethers since you don't seem to get a lot out of them. And stop doing all the pick-ups for her child. "Sorry, that won't work for me. Good luck!" is all you have to say. Actually, it's said that "No" is a complete sentence. You don't have to explain why you can't do things for her. Just say you cannot. If she persists, you can say that the boys have gone their separate ways and it's not a good fit anymore like it was when they were 5. Soften it by saying that kids often diverge in these later grades and have different interests, personalities, needs, wants, etc. If you want to (and she won't take it well, you can add that he's way too disrespectful and tries too hard to get his way. (Sounds better than "manipulative" but conveys the same thing.
The other thing that you and the other parents need to do is call her to come get her kid, or take him home, if he misbehaves. The host of that party should have stopped her at the door and said, "I'm so sorry, but this party is by invitation only and we just can't take walk-ins." But you can ONLY talk to her about your kid and your needs, and keep the other parents out of it. If she asks about another parent, tell her you have no idea and to ask them. The way to truly hurt her is to be the spokesperson for others and let her know everyone's talking about her behind her back. That's cruel and unnecessary.