No, it sounds as if you have started a new sentence halfway through your current sentence: "I write to my mother / A letter..."
Basically, "my mother" is the indirect object, and "a letter" is the direct object. Because you use "TO my mother", this clause must be placed after the direct object.
However, if you drop "to", you then put the indirect object before the direct object: "I write my mother a letter." That's the basic rule of placing indirect objects in a sentence.
You can simply write "I write to my mother" without a direct object in the sentence.