Oh he exists. Fucking Gil still owes me 100 bucks from that one time at Paco’s when he ate like 4 racks of ribs, and basically had a whole pitcher of margaritas to himself, then realized he “forgot” his wallet.
I don’t care if you tap him on the shoulder, or msg him on fb, or send him a smoke signal, you let him know I want that scratch back please. Thanks
I said “push on his arm”!! Doesn’t anyone read anymore?!! 
Update: I messaged this person again, admitted up front that I had simply been an ass, and apologized for being an ass.
Sounds like the right move; good on you!
Best decision possible.
As a follow on, in all seriousness, you need to take a serious look at why you immediately jumped on this woman in particular. Of course you’re stressed out about your wife’s health problems, of course you’re stressed about the financial impact those health problems will have on you both, of course there’s frustration that what is supposed to be an amazing honeymoon time is turning into something overwhelming.
I think you harbor a lot of guilt and anxiety over your love for this other woman, and a lot of genuine terror about what will happen if it comes out. That fear will poison every interaction between you, the other woman, her mother, and your wife. You need to work through those feelings, and if that means coming clean to your wife or cutting the other woman and her mother out of your life temporarily, you need to do it- because all your focus right now needs to be on you and your wife, not shadowboxing.
Because fb has the annoying messenger app. I won’t put that thing on my phone. So I can see someone sent a message, but I can’t see who it is or the message on my phone. I have to actually log in on my computer, which I rarely do. A heads up is appreciated.
To the OP, not only is it not a breach of netiquette (1999 wants it’s vocabulary back btw) your over the top reaction was waaaaaaay off base. And weird.
Woman sees post.
Woman posts “I’m sending you a PM”.
You rip into woman via PM.
You send non-apology PM.
You send apology PM.
At any point did she actually send the PM that got this disaster rolling?
I don’t recall anything like this in Netiquette, and I had a read through some of it not so long ago (because I think it’d be good to have more of it, and less of the awful behaviour towards each other).
Like most Facebook users I have broken Netiquette there far too often, but mostly the rule broken was “don’t waste people’s bandwidth on things that are not relevant or interesting to them” (which is why I now have people in lists and customise post privacy, so that I don’t bore every Tom Dick and Harry with posts aimed primarily at friends acquired through interest groups)