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As I have learned kanji, I have been under the impressions stroke order for box kanji like 日 should be left to right, top to bottom. Most kanji seem very consistent, or so I thought.
I recently discovered I have been writing 母 like I would 日、whereas it should be instead the first stroke is the left and bottom combined. Is either method technically correct? Or what rule will help predict this irregular stroke order?
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.
(generated here)
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.
Does the following explanation help?
The logogramme 母 is formed from 女 by adding two dots representing the prominent breasts typical to lactating women (while 女 epitomises a woman tempting a man.)
For the record the stroke order for 女 is indicated here -> http://jisho.org/search/%23kanji%20%E5%A5%B3 .
So (hopefully) you experience less difficulty in guessing the stroke order of the "composed character" 母.
Technically the correct order is left to bottom, and so on. You could do it in your own order, but I personally would not recommend that. 日 and 母 are very different characters to begin with. I would recommend using jisho.com for the stroke orders, as typed characters can be very distorted.
http://jisho.org/search/%23kanji%20%E6%AF%8D
The only way to really learn "irregular" stroke orders is to keep learning new kanji and memorizing their radical's stroke orders. I know that isn't exactly the answer you want, but there is no real way to predict irregular stroke orders except by finding patterns when learning new kanji.
However, once you learn the strokes of one radical, it will usually stay the same in whatever character it may be in. In your case, 海 and 毎 have very similar stroke order to 母 when making that "box-like" shape.
