Am I right to be upset??

Hello Ladies, I need some input. My bf has two children with his ex gf. Him and I dont live together he has his own place. When their relationship ended she moved out. Now she claims is hard for her to get the kids to their doctor's appointments cuz she located far from the clinic she attends. So every time the kids need to go to the doctor she wants to sleep over at my Bf's house. He claims he only allows her to stay because it allows him to spend time with the kids, and that he sleeps on the couch. Now am I wrong to be pissed off, keep in mind this is the same woman that e-mails nudes to my bf. Im glad he is open enough to tell me when she does things like that, but it pisses me off as well cuz he just deletes the pics and ignores her. I feel he should speak to her and make it clear he is no longer interested and that its unacceptable for her to countine to do that. Ladies am I wrong to feel fed up? Wth should I do??