From the etiquette viewpoint, who are you thinking that your daughter's friend is being rude to? It may be imprudent for her to post that--if many of her friends think she is "flaunting" a relationship that she shouldn't be, it may hurt her socially, but her kids know that she and their father are separated, and they're not likely to be seeing the Facebook status or pictures. If the kids know she's dating this guy, it's from other sources, either she told them or someone else did.
As Twik says, current etiquette doesn't expect people to pretend that everything is fine in a relationship until the divorce is final. Legal separation or no, this couple are no longer living together, and that's been made public. (There are people who choose to keep saying "Oh, she's fine" when asked about the people they're divorcing, and that's okay too, but it's not expected.)
Being public about her new boyfriend on Facebook might be a way of signaling (to her ex, or his parents, or some of her relatives) that no, she's not going to be getting back together with him, so they should stop trying to persuade her to do so. It's not subtle, but neither is having to keep saying "Mom/Dad/Cousin So-and-so, Bob and I are finished. He's still the father of my kids, and we're going to work together on that, but I'm not going back to him, so stop trying to convince me."