We can turn this into a homeschool science lesson and then it becomes on topic. 
Your recipie is acid based with the lemon juice and vinegar. I don’t know about Dr Bronner’s Sal Suds, though. Borax and baking soda are a base, which are fine cleaners too. But if you mix an acid and a base they will nutralize each other and you’ll lose their cleaning power. For example, everyone has probably seen baking soda and vinegar foam up when mixed. But what you’re left with is a somewhat neutral, powerless solution.
So it’s unlikely mixing some of those ingedients with your recipie would help.
That’s the whole reason dishwashers have a separate rinse aid cup. Most dishwasher detergents are a base and the rinse aid is an acid. The time release of the rinse cup keeps them separate for each cycle so they don’t cancel each other out.