I babysat a friend's child once who was a habitual screamer. The longest 3 hours of my life. I plastered on a smile as she & dp walked through the door having finally got him to sleep around 10 minutes before she drove up.
I salute you Pumble and there is little I can suggest that tops advice you've had already.
I have suggested Cry-sis to someone else who posted before Christmas, worth thinking about?
DH may not be able to come up with platitudes to reassure you but he's there now and he knows you and loves you. He isn't judging, these are out-of-the-ordinary times.
If you can get your parents or trusted friends to give you a break, seize it. Who gives a monkeys if they hear that DD2 is inconsolable at times. It does not mean you are bad parents! Until she settles it is what it is, a knackering, tough time and you and DH need that help. Or if nobody else is around: between you, you endure the grind, it feels endless but it won't be.
Dummy, bottle feeding, you may not have tried either with DD1, her sister might like them, could help.
Hope I don't offend you by saying this, parenting DD1 may have been a walk in the park compared to your second, but DD2 is still yours, still needs both parents. She may be a screaming fury at times but please don't read anything personal into it, it's not you.