He doesn't like structure or "rules." To organise a time for her to drop her son at his place is such a drama because he feels he is being controlled if she sets up a regular time. He has his own key to her house though he never lived there.
Fine if HE doesn't like rules, but he must respect other peoples' time, and understand the need for them to set up a time to meet and exchange the kid. The problem as I see it, is he doesn't respect the time of other people.
He continually plays the victim to her , i.e. he can't cope , he's depressed , I'm here in this country all alone etc etc.
He might very well have clinical depression, it's really common among artists. Or he might be the result of a socialist country, where he is not required to take care of himself, because the gov't does. Regardless, this is inconvenient for you.
I am not able to express my annoyance regarding him as that upsets her and she becomes insular and withdrawn when conflict arises.He just saps all the energy out of her and I sometimes feel that I am only left with the leftover pieces that he hasn't drawn out of her.
Her inability to talk about your feelings about her ex will ultimately destroy your relationship with her, IMO. Communication, and feeling like you are "heard", are very important. She does not appear to have these skills, regardless of how loving she is otherwise.
But don't take my word for it, just wait and see.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
(Please note, we give the best advice we can based on the information given in a post. For better advice, please include the age of all romantic partners.)