we have two phone lines coming into the house. one we do not use. it has the dual panel like you picture below.
the other line has 3 jacks. none of them have a two panel. they're just a square.
O.K., it sounds as though the line you are actually using was installed before BT adopted the NTE5 jack (the box pictured above). Either that or the wiring has been changed by someone since it was installed. The only way to isolate the extensions would be to open up the main jack and start disconnecting wires, which you probably don't want to do!
However......
it "seems" to be worse after a big rain storm
You're quite probably not imagining it. When a junction box leaks and lets damp in, it's very common for the problem to become more acute after heavy rain.
Given these symptoms, the chances are that the fault is with BT's outside line plant, in which case it should be repaired free of charge. The reason I was trying to isolate your extension wiring is that if you call BT repair and the fault turns out to be on your own internal wiring, then they'll hit you with a substantial callout fee.
I can't
guarantee that the fault is with BT, of course, but from your description it's the most likely cause.