J.S.
What's your question exactly referring to? I think that the most consistent factor in her and her childrens' lives is your partner because he sounds like a great father. It sounds as if even though he's not the biological father of her eldest son, he stuck it out with her and still had more kids with her and treated that boy as his own. Blood didn't matter to him. And that's why the boy gets to visit with his siblings. Your partner IS his father even if they don't share DNA.
The thing here is that while she's kind of overstepping, I don't think she's trying to get your man into her bed. But her children ARE your childrens' siblings. They are family and that makes HER family. And you and your partner treat her kindly and with respect. I'm sure that even though you don't feel she's family, that only the kids are, you treat her well and she feels like family. The men that come in and out of her life clearly don't do that. Why WOULDN'T she want to spend time with you guys? Why WOULDN'T she want her children to spend time with you and their siblings? You must have a very loving home. And in spite of your dislike or annoyance of her, you tolerate her and treat her kindly.
So here's the thing. You trust your partner, right? And it doesn't sound as if she's throwing herself at him. She's making poor decisions about dating, but she's trying to raise her kids and maintain a good parenting relationship with your partner and with you. She's infringing a bit, but she's not going to know what the boundaries are unless your boyfriend starts gently setting boundaries. Continue being kind and generous to her, but set more boundaries. See if you can set up a schedule or a routine so that there's less of the unexpected drop ins and visits.