We do sell the 82-081. This is a keyed version of your older handle, as well as having a somewhat updated style. The bad news is that it's not available in black. I'm afraid we cannot offer that color option. Otherwise, I'm confident that it will work for you.
Sure thing! So, the 82-081 is compatible with two different types of mortise latch: the 82-238 and the 82-268B. Between these two, I think you probably have the 82-268B. It's tough to say while it's still installed but there's a good chance that's what your customer has.
The reason I say this is because the side door trim totally covers the latch, which is common for this style. You'll have to pop the whole side trim of the door off in order to access the screws to remove it.
As long as your old mortise is working and in good condition, you can reuse it. Our 82-081 will be compatible with the mortise you have now.
I guess I'm still a little uncertain about the issue with the second door. Are you saying that the thumb lever isn't flipping? If it is, then the issue very well may be with the mortise lock. I can't say for sure. I would remove the handle and play around with the mortise to be sure. Try flipping the hooks manually with a screwdriver by turning the hole where the thumb lever goes. If you feel resistance or if it feels stuck, then you've found your culprit.