My boyfriend’s relationship with his cousin is shady

I have been dating this guy for almost a year now and the journey has been great. However, a couple of weeks ago, his cousin came back from the USA and her presence has been an absolute nightmare since. I am not the insecure type neither do I interpret things the wrong way. But there is something not right about his relationship with this girl. For starters, when we are out, she gets drunk and starts sitting on his lap, he never finds it odd. She always wants him to give her push to public bathrooms because for some reason she doesn’t trust them and I just do not see what my boyfriend’s presence will change. I once went to his place on a Saturday morning and found she had slept over; but it didn’t bother me, it was the ridiculously provocative piece of cloth she called ‘nightwear’ that did. Every time I make plans with him, he insists on bringing her along. I told him I wanted us to have some ‘alone time’ and he said she was here to visit and that he didn’t want to make it miserable for her so we would plan something after she left! I feel like the third wheel here. I have now resorted to turning down any plans to hang out for my own sanity’s sake and what is shocking is that my boyfriend didn’t even show the slightest concern. I might be wrong but something’s not right. Either she is not really his cousin or if she is, then the problem is much sicker than I thought. Please advise…