Lina -- It always amazes me how we all have such different thoughts on what makes a great bar of soap. For me, I've done a TON of experimenting over the years as I, too, have very sensitive skin.
What I've found is that my skin HATES soap made with ANY amount of coconut oil -- so I don't use it at all -- EVER!!! It gives my skin a strange, dry feeling that no moisturizing lotion can fix. Two other fats that give me that same dry feeling (when used in soap) are Babassu and Palm Kernal Oil. Surprisingly, regular Palm Oil does not do this, and I do use that in my soap. I also use about 12% Castor Oil to increase bubbles, and to create a moisturizing, stable lather.
My standard soap recipe (what I use every day):
32% Palm (NOT Palm Kernal)
32% Olive
12% Castor
12% Shea
12% Coco Butter
Superfat at 6%
For me, this soap is awesome, and makes great lather! I encourage you to experiment on your own.
I also highly recommend this soapmaking software (Soapmaker 3, $20) which is what I use:
https://www.soapmaker.ca/
Cheers!
Jim