First of all, evolution exists. Look it up. Wikipedia starts with the modern definition of biological evolution. Evolution means change over time. The thing that is changing is the relative abundance of different bits of DNA in a population over time. Anyone with the proper tools can go out and measure evolution. It takes incredible ignorance and denial to believe that evolution does not exist. Evolution is a natural phenomenon that is observable, measurable, quantifiable and predictable.
However, there is a great deal of scientific illiteracy and people do not understand how science works. I can't address all that is so distressingly wrong about your mom's reaction but it illustrates so clearly the difference between "knowing" by science and religion.
Before science, what people "knew" of the universe came from dogma. There were creation myths and just-so stories that explained how and why everything came to be. The absolute truth was already known and no questioning is allowed.
By contrast, science deals with the limitation of our understanding. Scientists realize that what we do understand is only a tiny portion of what is going on in nature. Scientists always put limits on how far they can apply the models (theories) and always realize that these models can fail if pushed beyond these limits. Scientists use the tools of critical thinking to increase our knowledge and understanding where as the religious view is that the truth is already known and there is no questioning of the good word.
The religious also attack the person most associated with evolution as if that somehow invalidates the entire body of knowledge collected over 150 years. Why would Darwin saying "Never mind, I take it all back" have any bearing on all that we have learned and improved upon to better understand biological systems? [BTW, look up when video and audio recording devices were invented. This is a lie spread by fanatics to attack Darwin's work. The religious are notorious for lying, torturing, killing to silence those with opposing viewpoints]. Scientists do not have prophets where the ultimate truth is laid down and must be obeyed for all time. We are using the previous work of great thinkers and extending it, making their ideas better.
We do not celebrate Darwin because he knew everything about biology and gave us the Gospel of Charles. Darwin didn't know anything about modern biology. He did not know how traits were transmitted between generations. He knew nothing about molecular biology which provides the strongest evidence for evolution by natural selection. We celebrate him because every new discovery in biology, every experiment run over 150 years is consistent with the ideas he first proposed.
The religious viewpoint is to venerate prophets. Religions have special persons gifted with a privileged knowledge. These prophets/priests have the true understanding and we are told to accept their teachings forever and ever. If a prophet recants on his death bed, then the religious story falters so it is reflexive for the religious to do the same of scientists.
Newton was wrong. His model of the universe breaks down when pushed to high velocity, or small sizes or strong gravitational fields. Einstein came along and improved Newtons model. But, even Einstein's model is wrong. It breaks down at small distances. But, we don't try to make up stories against Einstein or deny Relativity to keep to the dogma of Newton. Scientists are constantly trying to push their models to the limit where they fail. Scientists WANT to find situations where the Theory of Evolution by Natural Selection does not work. Scientists seek situations where theories fail because that is the way we discover new things. That is the only way to push our understanding of the universe. If someone found a situation where the Theory of Evolution by Natural Selection did not work, then it would be celebrated. It would be Nobel Prize worthy. The news would be splashed about for all. Don't you think that if the Theory of Evolution by Natural Selection was clearly demonstrated to fail, more people than just the religious and scientifically illiterate would know about it? It is taught because Evolution is a Fact. Evolution happens. The BEST explanation for how and why evolution happens is the Theory of Evolution by Natural Selection. This theory is the foundation of all modern biology which is why it is still taught.