Is this unreasonable?

My first reaction is "wow, nurses have so much time on their hands that they can just wander around and chat with other patients' families?" That is certainly not the case in most hospitals these days.

Second impression - as a Critical Care nurse, I cannot even imagine a nurse just jumping in and medicating someone else's patient without checking with him first. That's a huge no-no. Managing complex care is already challenging enough.... no need to add random interactions to the mix. You don't have to be an expert to see that it won't end well. If this is happening with multiple nurses, I urge you to bring it up with your manager... and work on coming up with a solution. If it's just one 'Chatty Cathy', talk to her about it. If that doesn't work, ask your manager to step in.

You are not being unreasonable.

Sadly many nurses have issues with personal/professional boundaries and telling personal stories/opinions to frightened patients and families rather than empowering them to ask the right questions

I could handle the Chatty Cathy, but another nurse coming and medicating my patient?!?! Uh, no. Not okay.

The stories and poor practice would bother me. However I would not want to create an environment where being a team player is frowned upon. I expect that any other nurse on my unit is competent to adjust meds if I am tied up.

So if they are doing it incorrectly, they need some education. That benefits everyone.

I re-read the OP and it sounds like she gave report to one nurse, but another came in and over sedated her patient? Not sure now. At first I thought she had said that some nurse just happened to be walking by, saw the patient bucking the vent, and took it upon herself to medicate. Doesn't seem like that is the case.