Re the immediate issue re dual notice it’s trivial to make a combo number header so the text goes to both of them automatically with no additional work on your part. Just arrange that you can text them or call them re notice.
Well played. There truly is an XKCD for every occasion.
So without a jurisdiction, it’s pretty much impossible to give any targeted advice, as labour laws vary incredibly. I’ll just tell you what my 20 years of experience tells me.
Your bosses suck.
Your bosses are not going to change.
Polish up your resume and start job hunting.
Refusing to sign a write-up will not help you, and may in fact hinder you. (Insubordination is a valid reason for them to fire you.) You can put “signing to indicate receipt only” on the write-up instead.
It’s impossible to state what will happen if they fire you without knowing your jurisdiction. In Canada, being fired for cause will make it difficult to get employment insurance. Things are very different in the US due to at-will employment, so I can’t comment on that.
If the owner doesn’t, no one else cares if your company or manager is “acting reasonably.” Unless they are discriminating on strictly defined legal grounds (race, gender, religion, etc.) or breaking labour laws, no one cares. It is not illegal to be a total jackass of an employer.
Let me turn this around on you just a bit:
Unreasonable management - how far can you be pushed?
Only you can determine the point where it’s just no longer worth it. If you’re not there yet, they can push farther.