Any Electrical Help Out There?

Attention All Electricians Out There!  I need some help here!

What you see to the left is the junction box for our Staff House?  If I have it right, the Main Power comes in on the Right Side.

We also have a Generator.  Somehow or another, there's a safety built in so that when the Main Power comes on (a few hours a day at random times) it doesn't affect our generator.

Ok..When the generator comes on, (I think the contraption on the Left), the little button on the contraption goes in and the contraption on the Right...that's a switch of some sort...a bridge-like thingy that closes the circuit and provides power for the house from the generator.

Now notice the next picture and my problem:

There should be a really heavy gauge wire from the top-right of the Left contraption to the top-left of the Switch on the Right.  Someone used wire that was way too small.  I suspect that as that wire got hot it eventually burned up the connection on the top-left post on the Switch.

Here's the Question:  What the heck kind of switch is this?  Could some other kind of switch work?

Can someone find something that will work and send it to us?  We have teams coming down every week and someone could bring us what we need.

Right now, we have disconnected the Main Power- we are completely off the Grid to avoid a conflict with our generator and the main power source...which means we are completely dependent on our generator.  That's gonna get expensive and it's a heck of a strain to run the whole house on it.

Let me know if you can help: email me at Clinton@clintonwhite.net