Agree your DS should apologise to you for his aggression and abusive language. 100% not acceptable. Understandable you were affected.
However, are you planning to apologise to your DS for joking about this?
Having a laugh is important, but doesn’t set a good example to joke about violence or death. Why do it? It may not be meant to cause harm, but if you say that to a person who (possibly unbeknownst to you) is feeling so depressed and anxious they might feel like they want to die, it can be very harmful.
Also, might be helpful to reflect on why you told him to leave and go to his father’s home. IMHO would be better to deal with it yourself: (if safe) calmly suggest he goes to his room until he’s calmed down or remove yourself from his presence, rather than send him to his other parent to deal with. It can be damaging for kids of any age to be rejected by a parent. It’s best they stay at home when feeling like that. If you ask them to leave the house, they may be a danger to themselves.
Also, might help to treat him as a young adult rather than telling him what to do like a child. If his elder brother needed the dryer, he could’ve asked him directly to move his stuff. Was there any need for you to intervene? If he ends up with musty laundry, it’s his choice. In a calmer moment you could explain how to operate the dryer correctly. Also, it’s pretty impressive these days for a 16yo to be dealing with their own laundry. Helps to give credit where it’s due: praise rather than criticism.
Ignore your ex. He’s definitely being abusive and likely bad-mouthing you to your DS. He’s basically capitalising on a fairly typical parent-teenager scenario.
Arrange to meet with your DS somewhere neutral and hear what he has to say first. Truly listen to his pov with humility. Tell him you love him and want him home. Show him you regret how you acted (if you do). But be firm that, as a man, it’s important he learns ways not to be aggressive or abusive when frustrated or aggrieved. Walk away, breath deeply, distract himself (with music, tv etc) and chill.
With my teen/young adult kids, it helped afterwards to see the funny side about how we both behaved to relieve tension and avoid on-going resentful. None of us are perfect all the time. On that note, hopefully it’ll all come out in the wash.