You can do almost what you want if you find the right functions available in physlet library and javascript codes.
Check out http://webphysics.davidson.edu/Applets/PhysletsDoc/index.html for information about physlet available functions.

You have the following javascript physlet code:
id1=fkh.addObject("coil","x=0,y=0,i=1,r=0.1");id2=fkh.addObject("coil","x=0.02,y=0,i=1,r=0.1");id3=fkh.addObject("coil","x=0.04,y=0,i=1,r=0.1");id4=fkh.addObject("coil","x=0.06,y=0,i=1,r=0.1");id5=fkh.addObject("coil","x=0.08,y=0,i=1,r=0.1");id6=fkh.addObject("coil","x=0.1,y=0,i=1,r=0.1");id7=fkh.addObject("coil","x=0.12,y=0,i=1,r=0.1");id8=fkh.addObject("coil","x=0.14,y=0,i=1,r=0.1");id9=fkh.addObject("coil","x=0.16,y=0,i=1,r=0.1");id10=fkh.addObject("coil","x=0.2,y=0,i=1,r=0.1");id11=fkh.addObject("coil","x=0.18,y=0,i=1,r=0.1");id12=fkh.addObject("coil","x=0.22,y=0,i=1,r=0.1");id13=fkh.addObject("coil","x=0.24,y=0,i=1,r=0.1");id14=fkh.addObject("coil","x=0.24,y=0,i=1,r=0.1");id15=fkh.addObject("coil","x=0.26,y=0,i=1,r=0.1");id16=fkh.addObject("coil","x=0.28,y=0,i=1,r=0.1");id17=fkh.addObject("coil","x=0.28,y=0,i=1,r=0.1");id18=fkh.addObject("coil","x=0.3,y=0,i=1,r=0.1");

where id1,id2,...id18 are integer variables. from the above web page you can find
double getX(int id):           Get the x position of an object.
boolean setX(int id, double x)          Change the x of an object.
So if you only set id1 dragable with code
fkh.setDragable(id1,true);

Then, you can use x1=getX(id1); to get x coordinate for the dragged coil
then you can add
setX(id2,x1+=dx);
setX(id3,x1+=dx);
....
to set all the coils.
If you want user to drag coil in horizontal only. add the following code
setY(id1,0); // to fix y coordinate for the first coil


It will be easier if you use array object
for examples:
id=new Array(18);
x1=0;
for(i=0;i<18;i++){ // use this loop to create coils
id[i]=fkh.addObject("coil","x="+x1+",y=0,i=1,r=0.1");
x1+=0.2;
}
Then it will be easier to move all the coil together
x1=getX(id[0]); y1=getY(id[0]);
for(i=1;i<18;i++){// move all the coils (x,y) together
setX(id[i],x1+=dx);
setY(id[i],y1);
}