This character, 令 looks one way in text/font, and in my RTK book.

But Jisho has a little animation that shows stroke order, and the bottom element here looks completely different in that hand-written version. Still two strokes, but a different resulting shape.

The same applies to other kanji that build from it, like 冷, 零, etc.

What's the story? Is one or the other source wrong, has the character been updated to a new form, or do I just have wrong fonts?

It's basically just different fonts. Your handwriting probably doesn't look exactly like the letters you see on screen, does it? Follow the stroke order in Jisho when writing by hand.

Found this page with some info on it: https://japanese.stackexchange.com/questions/92926/rei-令-handwritten-variant

I've run into issues of fonts using Chinese version of characters instead of Japanese, but in this case it seems like this character is just written differently in some contexts.

japanase and simplified/traditional chinese differences, wictionary is good for looking and the different variants
https://en.wiktionary.org/wiki/令