I think Nicki is firmly into the headspace that many 'influencers' seem to enter after a while of doing it full time - that this isn't just a job anymore, it's a lifestyle and they basically have no choice but to do it. It's not true, but it's a mental justification for their often unacceptable behaviour.It's really sad for Carlo and his blood family.
His wife however hadn't seen her FIL for a while because recently, while he was ill, she allowed her husband to go back to Positano alone because, rather like a child with a new toy, she didn't want to leave the Tuscany house. Selfish. Feel any remorse that she didn't take the opportunity to to see him while she could? Of course not. I bet she's fuming that she's had to stop playing move the furniture and support her husband instead.
I find it irritating that she does a piece to camera about how some things need to be kept private, launches into this diatribe about how she doesn't really want to address it. She could have simply put a message up saying his father had passed away. She explains it like we're all stupid and can't understand the gravity of the situation when really she's just projecting.
Now I absolutely believe we all deserve a certain amount of privacy, but like you said, it's this condescending attitude from her that is the problem. The truth is she could pick up a job in a supermarket and fade into absolute obscurity again. She could have permanent privacy. But like any job there are pros and cons, and the pros AND cons of vlogging are that you are making money off showcasing your life rather than working a set shift and leaving it after X amount of time. I don't understand why she thinks this is unfair. It is the nature of the job and if privacy means more to her than the no boss, no set working hours, ability to take holiday when you want, no office politics etc - then she needs to look for a new job.