Splitting the total sum based on dropdown options selected

Yes, you can achieve this functionality with a custom script. You'll need to write JavaScript to differentiate between "Trip" and "Vacation" options and then update the respective totals accordingly. You can attach event listeners to the dropdown options and update the totals dynamically based on the selected option.

Agreeing with Thom that Total Days columns isn't helpful.  Change the export values to either "Trip", or "Vacation".  Enter the following script as a custom calculation script in the Total Trip Days field:

var trip=0;
for(var i=1;i<15;i++)
{
if(this.getField("Dropdown"+i).value=="Trip")
{trip+=1}
}
event.value=trip;

Enter the same script in the Total Vacation Days field but change "trip" to "vacation" and "Trip" to "Vacation".

Separating trip days from vacation days requires analyzing the dropdown values.  To do this it is helpful to name the fields so that the field set of interest can be easily acquired. For example, if the fields in the "Description" column were named "Description.Row1",  "Description.Row2", etc. then the selected values could be easily acquired. 

Also, the total days field is not helpful, since it will always be 1 day.  It would also be better for the caculation if there was no export value. 

And the calculation scripts could be written like this.

// Custom calculation for Trip days total

var nSum = 0;

this.getField("Description").getArray().forEach(function(oFld){if(oFld.getItemAt(oFld.currentValueIndices,false).indexOf("Trip")>-1)nSum++;});

event.value = nSum;

Haven't debugged this so open the console window before testing it to see if any errors are reported when it was run. 

The code could be simplified if the export values were removed from the description dropdown, or if they were changed to numbers that represent the Trip/Vacation split.