1. import peasy.*;
2. 
   
3. PeasyCam cam;
4. 
   
5. void setup() {
6.   size(300,200,P3D);
7.   cam = new PeasyCam(this, 0, 0, 0, 100);
8.   cam.setMinimumDistance(50);
9.   cam.setMaximumDistance(500);
10. }
11. void draw() {
12.   
13.   //3D object
14.   rotateX(-.5);
15.   rotateY(-.5);
16.   background(0);
17.   fill(255,0,0);
18.   box(30);
19.   
20.   //2D object that is not affected  by the camera
21.   camera();
22.   fill(0,0,255);
23.   rect(200, height/2 -25 , 50, 50);
24. }

1) beginHUD() + endHUD()
2) camera.lookAt(x,y,z) where (x,y,z) is the position of the object you want to rotate around

Example code:

1. import peasy.*;
2. PeasyCam cam;
3. 
   
4. void setup() {
5.   size(300,200,P3D);
6.   // either put it here like this:
   
7.   // cam = new PeasyCam(this, 50, 0, 0, 100);
8.   cam = new PeasyCam(this, 0, 0, 0, 100);
9.   cam.setMinimumDistance(50);
10.   cam.setMaximumDistance(500);
11.   // or separate like this:
    
12.   cam.lookAt(50,0,0);
13. }
14. 
    
15. void draw() {
16.   background(0);
17. 
    
18.   //3D object
19.   pushMatrix();
20.   fill(255,0,0);
21.   translate(50,0,0);
22.   rotateX(-.5);
23.   rotateY(-.5);
24.   box(30);
25.   popMatrix();
26.  
27.   //2D object that is not affected  by the camera
28.   cam.beginHUD();
29.   fill(0,0,255);
30.   rect(200, height/2 -25 , 50, 50);
31.   cam.endHUD();
32. }

I see what your mean. I think that's hard to do with PeasyCam because it's completely based on rotation around a look-at point. Or as it says on the github:

The PeasyCam is positioned on a sphere whose radius is the given distance from the look-at point. Rotations are around axes that pass through the looked-at point.

As I understand it, you want to rotate around one point (the center of the object) and look at another point (NOT the center of the object). However in PeasyCam these two points are not different, they are always the same. The point you rotate around is the point you look at. Or more accurately, the point you look at is the point you rotate around. There is no way to distinguish between them. That's just the way the library is made.

So perhaps in this case going with some of your own code (for example using translate and rotate) is easier.