It is easier to add water. Goat milk discolors if you add it when it is too warm and can make your trace more difficult, the issue that you had with the batch you broke the mixer on.
I doubt you jumped into your clinicals without any background knowledge, it is the same with soap. Learning how to pour it into the molds, unmold it, recognizing trace, learning how to not burn out your mixer, etc., takes time and practice. It is easiest to start with easy simple soap and progress from there. You are asking for help but you are jumping into the hardest things first. I tried two batches before I tried goat milk soap. I didn't want to waste oils. After those turned out, I tried adding more ingredients to the soap. I still have not tried a different oil. I certainly have not made up my own recipe yet. So soap has been easy and fun for me.
We are trying to explain how to learn, by doing an easy and fun one first. You can certainly jump into more difficult ones first. But you might have more frustrations and have more that doesn't turn out.
Perhaps you feel you must try the hardest things right off the bat because doing anything less is a waste. I can assure you, my homemade non goat milk soap was much nicer than anything else I had ever used. It was well worth the trouble. I did add fragrance and it came out very nice, I used it as gifts.
But if you are willing to waste ingredients, you can start off doing the hard recipes. If you are willing to spend money that way, however, you might tray buying a couple basic soapmaking books. There is a lot of ideas and recipes of how to make soap, a good book will give you a better overview of the concepts we are trying to explain to you in quick blurbs. The recipes are just tried and true combinations that someone else ahead of you has created a nice soap balance. It is like making a cake, if you want certain qualities, you use a recipe that gives you those characteristics. The more you understand the recipes, the closer your final result will be to what you were working towards. Adding colors and swirls and scents and interesting molds are all things that make it harder, and using goat milk can make the soap discolor. So this is why you are getting suggestions for trying an easy recipe first.