I have an instance of a class, I want to change an object data member of this instance only with another object of the same type (swap), due to my system c
Yes, its possible.
In short, do something like
Type typeInQuestion = typeof(TypeHidingTheField);
FieldInfo field = typeInQuestion.GetField("FieldName", BindingFlags.NonPublic | BindingFlags.Instance);
field.SetValue(instanceOfObject, newValue);
to change the value of a hidden (private/protected/internal) field. Use the corresponding FieldInfo.GetValue(...) to read; combine the two trivially to get your desired swapping operation.
Don't hold me to the BindingFlags (I always seem to get those wrong on the first attempt) or the exact syntax, but that's basically it.
Look over System.Reflection for reference.