I would like to say...
My Mom did not get angry as much as my Dad did.
...but I want the sentence to also convey that I had expected my Mom to be more angry (not less) than my Dad.
How can I say this in natural English?
When you're trying to illustrate the difference between what you expected and what actually happened, you need to use words like "but", "however", "contrary", or "unexpectedly" to provide that contrast.
I thought my mom would be angrier than my dad, but it was the other way around.
Contrary to my expectations, my dad was angrier than my mom.
How about "in spite"?
In spite of my expectations, Mom was not as angry as my dad. Or perhaps despite?
de·spite dəˈspīt/ preposition 1. without being affected by; in spite of. "he remains a great leader despite age and infirmity" synonyms: in spite of, notwithstanding, regardless of, in the face of, for all, even with "despite his lack of enthusiasm, Zachary had a pretty good time"