FWIW, I don't think FMIL was criticizing, I think she was trying to offer advice. She knows I have next to no experience with kids. I also think she and my mother are from the same stock and thus they don't think about how the way they say things come across. It wasn't a debate, either, just each of us discussing why we did/would have done it one way or the other. I don't think she thought about sympathy pukers, either.
This does not surprise me.
I don't think she was talking manners or etiquette--she was talking tactics and strategy.
And, I have found throughout the years that:
1) your first response isn't always the most -effective response;
2) panicking, or moving too fast, is often not the most -effective tack;
3) the best thing to do w/ messes like that is to make sure they fall on things that can go in the washing machine (like the front of your own shirt) or that can be mopped off (like a linoleum floor)
When my kids were babies, I quickly figured out that if they were going to have a big spit-up it was best if they did it all over me--because the sofa can't go in the washing machine, but my shirt can (and skin washes really really well).
So when they threw up, I did the same thing--I held them so it splashed all over me.
Rushing to the bathroom might not be the best bet--it's smartest to slow down a little, and make sure you have a game plan for the "instant vomit" that might still be coming. Like, you whip off your jacket and hand her the hood to use, and you steer her on her own two feet instead of carrying her so that your hands and arms are free to help hold the "bucket".
But of course, who can think that well right then, right? And, maybe what you did was your best plan of action--I don't mean to backseat drive you, just pointing out the concept of "don't panic; think it through a little bit first" and how valuable it can be.
My toddler son got hot tomato sauce dumped right on him at a Red Lobster; I picked him up and ran to the bathroom to strip him off. It was actually not the smartest move; it took too long to start getting the clinging, hot sauce off him.
I should have simply picked up a water glass and poured it over him. It might have been messier on the floor, but the point wasn't the mess, it was the heat.
In your case, the point was the mess; containing that would be the big plan.
What you did was perfectly fine in terms of etiquette. You did the best you could.
In terms of effectiveness, there might have been something else you could do, but I sure wouldn't suggest you beat yourself up about it. But, us parents would probably all benefit from mentally walking through some of those things:
-what if my kid suddenly started throwing up?
(My sister sacrificed her purse when she got sick on the merry-go-round; she figured it was replaceable. It was--my mom bought her a new one.)
-what if my kid got something hot spilled on him?
-what if my kid cut himself?
-what if my kid tipped a milkshake over?
So we have a plan.
The milkshake thing--most of us have spilled stuff, so we have a subroutine we can tap. Puking kids, not so much.