Steve. Ive done lots of sink traps. The nut that is on the side closet to the wall meaning faryhest away before it goes into the wall turns the opisite direction as the ones on the sink side of the trap.
It sounds like you are dealing with an old metal trap. If I was you Id cut it apart however you can. Leave the pipes that come striaght down from the sinks as until the first nut that is part of the strainer in the sink.
At the wall, you want to leave as much as you can coming out of the wall. Then go to a hardware store and buy a new plastic trap kit. Take pictures and show the guy selling the plumbing stuff. He should be able to help. They make a rubber adaptor that you tighten onto the pipe at the wall. Then add a pipe that comes to the trap. With a disposal and dishwasher its a bit different for each install. Dishwasher goes into disposal normally. Second sink goes into disposal. Then out of disposal to trap.
You Tube it!
I bet you will find all the info you need. But get that old stuff out and buy plastic not chrome.
PM me if you need more help.