Photoshop Distribution by custom width parameters

Ha! I found the script and found another script that does what you want, except that it doesn't center the middle layer. It just spaces all the layers on a custom value in pixels. Here it is. For it to work, you have to select the layers that you want distributed.

#target photoshop
app.displayDialogs = DialogModes.NO; 

if (app.documents.length>0){
      var dlg = new Window('dialog','Space Objects');
      var docRef = activeDocument
      var shapeSizeTotal = 0
      var selLay = getSelectedLayersIdx()
      var docLayers = new Array()
      var isHor = true;
      var amt;

      if (selLay.length>2){runProg()}
      else{alert('There needs to be 3 or more layers selected')}
}
else{alert('There are no open Documents')};

function runProg(){
      var run = true;
      dlg.hor = dlg.add('radiobutton',undefined,'Space Horizontal');
            dlg.hor.value = true;
      dlg.vert = dlg.add('radiobutton',undefined,'Space Vertical');
      
      dlg.infoGp = dlg.add('group');
      dlg.sTxt = dlg.infoGp.add('statictext',undefined,'Enter the distance between the objects (' + app.preferences.rulerUnits.toString().replace(/Units\./, '') + '):');
      dlg.eTxt = dlg.infoGp.add('editnumber',undefined, '');
      dlg.eTxt.size = [100,20]      
      
      dlg.buttonGp = dlg.add('group');
            dlg.buttonGp.okay = dlg.buttonGp.add('button',undefined,'Okay');
                  dlg.buttonGp.okay.onClick = function(){
                         dlg.close();
                         if(dlg.hor.value){isHor = true}
                         else {isHor = false};    
                         amt = dlg.eTxt.value
                        }
            
            dlg.buttonGp.cancel = dlg.buttonGp.add('button',undefined,'cancel');
                  dlg.buttonGp.cancel.onClick = function(){
                        dlg.close();
                        run = false;
                        }
                    
      dlg.eTxt.active = true;
      dlg.show()

      if(run){
            makeActiveByIndex(selLay, true)
            docLayers.sort(compare)

            for (var i=0;i<docLayers.length-1;i++){
                  if(isHor){
                         var deltaM = amt-(docLayers[i+1][1].bounds[0].value-docLayers[i][1].bounds[2].value)               
                         docLayers[i+1][1].translate (deltaM, 0) 
                         $.writeln(deltaM)
                        }
                  else{
                         var deltaM = amt-(docLayers[i+1][1].bounds[1].value-docLayers[i][1].bounds[3].value)               
                         docLayers[i+1][1].translate (0, deltaM) 
                        }
                  };


            makeSingleActiveByIndex(selLay[0], true);//select only one layer to make the translations
            //docRef.activeLayer = docRef.layers[docRef.layers.length-1]

            makeActiveByIndex(selLay, true);//reset selection to all layers
      }//end if to run
};//end function runProg

function compare(a,b){return a-b}

function getSelectedLayersIdx() {
    var selectedLayers = new Array;
    var ref = new ActionReference();
    ref.putEnumerated(charIDToTypeID("Dcmn"), charIDToTypeID("Ordn"), charIDToTypeID("Trgt"));
    var desc = executeActionGet(ref);
    if (desc.hasKey(stringIDToTypeID("targetLayers"))) {
        desc = desc.getList(stringIDToTypeID("targetLayers"));
        var c = desc.count
        var selectedLayers = new Array();
        for (var i = 0; i < c; i++) {
            try {
                docRef.backgroundLayer;
                selectedLayers.push(desc.getReference(i).getIndex());
            } catch (e) {
                selectedLayers.push(desc.getReference(i).getIndex() + 1);
            }
        }
    } else {
        var ref = new ActionReference();
        ref.putProperty(charIDToTypeID("Prpr"), charIDToTypeID("ItmI"));
        ref.putEnumerated(charIDToTypeID("Lyr "), charIDToTypeID("Ordn"), charIDToTypeID("Trgt"));
        try {
            docRef.backgroundLayer;
            selectedLayers.push(executeActionGet(ref).getInteger(charIDToTypeID("ItmI")) - 1);
        } catch (e) {
            selectedLayers.push(executeActionGet(ref).getInteger(charIDToTypeID("ItmI")));
        }
    }
    return selectedLayers;
}

function makeActiveByIndex(idx, visible) {    

      for (var i = 0; i < idx.length; i++) {
            var desc = new ActionDescriptor();
            var ref = new ActionReference();
            ref.putIndex(charIDToTypeID("Lyr "), idx[i])
            desc.putReference(charIDToTypeID("null"), ref);
            if (i > 0) {
                  var idselectionModifier = stringIDToTypeID("selectionModifier");
                  var idselectionModifierType = stringIDToTypeID("selectionModifierType");
                  var idaddToSelection = stringIDToTypeID("addToSelection");
                  desc.putEnumerated(idselectionModifier, idselectionModifierType, idaddToSelection);
            }
            desc.putBoolean(charIDToTypeID("MkVs"), visible);
            executeAction(charIDToTypeID("slct"), desc, DialogModes.NO);
            
            if(checkLayerKind(docRef.activeLayer)){  
                  if(isHor){var layerLeft = new Array(docRef.activeLayer.bounds[0],docRef.activeLayer)}
                  else{var layerLeft = new Array(docRef.activeLayer.bounds[1],docRef.activeLayer)}
                  docLayers.push(layerLeft)
                  }
      }

};// end makeActiveByIndex

function makeSingleActiveByIndex(idx, visible) {
      
            var desc = new ActionDescriptor();
            var ref = new ActionReference();
            ref.putIndex(charIDToTypeID("Lyr "), idx)
            desc.putReference(charIDToTypeID("null"), ref);
            /*if (i > 0) {
                  var idselectionModifier = stringIDToTypeID("selectionModifier");
                  var idselectionModifierType = stringIDToTypeID("selectionModifierType");
                  var idaddToSelection = stringIDToTypeID("addToSelection");
                  desc.putEnumerated(idselectionModifier, idselectionModifierType, idaddToSelection);
            }*/
            desc.putBoolean(charIDToTypeID("MkVs"), visible);
            executeAction(charIDToTypeID("slct"), desc, DialogModes.NO);

      
};//end makeSingleActiveByIndex

function checkLayerKind(lay){
      if(lay.kind == LayerKind.NORMAL || lay.kind == LayerKind.TEXT || lay.kind == LayerKind.SOLIDFILL){return true}
      else{return false}
      
      };//end checkLayerKind

I would say you need a script for that. I wrote one back before Adobe released the distribute with even spaces, but it would just be a matter of using input for the spacing rather than dividing the space between the objects.

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible? 

I suspect this would need a Script, but that might need additional checks/rules in case the left and the right distance between the three layers are actually not exactly identical.