The fact that the topic in question is tznius (modesty) makes things even a bit more complicated, as there are multiple aspects to this mitzvah. First, the mitzvah has both an objective as well as a subjective element to it. As an example of objective immodesty, the Gemara states (Berachos 24A) that a woman’s thigh is considered to be an area that must be covered. There is some debate as to whether this applies below the knee, and the Mishneh Berurah rules (Orach Chaim 75, note 2) that it is not necessary to cover below the knee. However, the Mishneh Berurah notes subjective tznius factors as well, including local custom. Thus there are parts of the body such as the upper thigh and chest that must be covered in public no matter where one lives and what the circumstances are, while others such as below the knee and sleeve length often depend on circumstance.
It is critical to note as well that modesty refers to a great deal more than length of fabric, as its fundamental focus is upon not making oneself an unnecessary center of attention. One should look at the style of the clothing - is it tight and flashy or more quiet and unassuming? Dress is only one dimension of modesty: tznius also very much applies to behavior and speech. Does one act and speak in a way that draws attention without cause?
One of the first steps that the great Poskim (halachik deciders) utilize in such conflicts of values is to consider whether there is a way to frame the situation that the values need not be in conflict in the first place. To wit, are you actually being asked by your mother to violate the mitzvah of tznius? Is she requiring you to wear shorts or tank tops during the summer? Many women who are meticulous about the mitzvah of modesty and live in warm climates wear lightweight fabrics that cover their bodies without being overly uncomfortable in hot weather and find that one or two layers is quite sufficient. Might there be solutions that would allow you to adhere to your values of dressing modestly while allaying your mother's apparent concern about your well-being? If you are able to have a conversation with her in which you let her know that you care about her concerns and would like to try and find a way to respect them, she may have ideas that are acceptable to you. By asking the question in a respectful way, you will also be demonstrating the idea that "the ways of [the Torah] are pleasant" and will be fulfilling the mitzvah of Kiddush Hashem (sanctifying Hashem’s name) at the same time that you fulfill the mitzvah of honoring your parent.
Assuming that you are new to the Orthodox life, I think your mother is correct; honoring her wishes is certainly one of the most important precepts—especially since she does not mind you dressing like a Modern Orthodox young woman. Your mother has every right to make this demand since you are already acting in accordance with Jewish tradition and law.