Some characters indeed have tricky stroke orders even for native speakers (writers?), for instance, 左 is started from the horizontal line but 右 is from the slanted one, and so on. But in your case, it seems to be a simple misunderstanding.
I don't know which font you use to browse this site, but typically, 母 and 日 would look like in the image below, respectively.
Note that 母 has two lines crossed at its bottom-right corner, which indicates that it's different than what you called "box" structure such as 日. Each writing system obviously has its own crucial points of recognition however they look tiny to you, as (if I assume you only read Latin alphabets) in Cyrillic alphabet м and т differs soundly (I hope you're using a font displays their true italic forms, but if not, please refer here for what I mean), and in hiragana わ, れ and ね. As well as in kanji.
Blaming etymology is, technically, kind of circular reasoning in this discussion, because today's standard kanji shapes incorporate more or less calligraphic or handwriting feature, that is, they're actually shaped like how they wrote them. It's better to just think it as the same reason why we don't write O like D.