I thought your reaction to the immediate situation reasonable…and hopefully she knew what was happening beforehand; randomly finding blood on you will freak most people out, but not knowing why is even scarier especially for a young girl.
Sharing the situation with two mothers I know that have daughters past that point (was interested on their take) ; they were pretty much in the same boat, they felt you acted right, although of course they both said they’d prefer to be there rather than the hubby; but if not, really the only concern was: ‘was the daughter bothered by it?’ (Although the one said you should have called the grandmother and the other said the daughter would likely want to crawl up and die if you did….so maybe an experience thing lol.)
It’s an uncomfortable subject, but you were the only one on hand to explain it, hell I’d give you bonus points for the youtube idea so you don’t have to go into every private detail and have her burying her head in embarrassment from you having to explain every detail in person.
I think the general: ‘it’s no problem’ attitude is really the way to take it; ‘Here’s what’s happening, here’s some pads, here’s a youtube video how to use them, take your time in private, and then let’s do what we normally do’.