In the baby swing most of the time and slept in it at night too? There's your issue right there.
Honestly? If it were me, I'd give the parents an ultimatum of working on safe sleep and giving them 2 weeks to show signs of improvement. Sure, it's going to be tough. And loud for them and you. BUT they are the ones who have set this poor baby up for failure.
I had a dcm who would nurse her baby to sleep every single time, course when mama wasn't there and he'd wake up, she'd magically reappear to put him to sleep in that manner. No matter if it was 15 minutes ago or an hour. If that didn't work, she'd put him in the bouncer for naps/sleeping at night. Needless to say he could not fall asleep by himself. It took 5 weeks of him crying the whole nap time through and the parents finally letting him cry a bit at night, before he learned to do it on his own. And he was, I want to say, almost a year by then. Now, he's the first 1 out like a light, with no crying whatsoever.
The parents have GOT to work with you on this. Honestly. Mark your calendar and tell them if he doesn't change, you'll have to let him go. It affects everyone. Constantly crying babies creates so much stress and it's just not feasible in a home dc atmosphere.