Reminders don't transfer and there's not a way to make them do so that I'm aware of. We have a similar "issue" with our shared family calendar. We both add to it so we know what each other is up to and/or when we have my stepson on days we wouldn't normally, or when he has school functions that we both should attend, etc.
Anyway, it doesn't matter what reminders either of us sets on our own device. As far as I can tell, the reminders are device specific, meaning they only function on the device that you use to add the event to the calendar.
It's kind of a double-edged sword really, because I don't need the Mrs.' reminders for her work schedule and when I put things on there from my phone, she gets them, but I can see how you'd want certain reminders to pop up regardless of which device you use.
A few options:
There may be another third party calendar app that can sync notifications between devices, but I'm not aware of one off the top of my head, since it's not really a problem that I have, but a situation that I've noticed.
A slight work-around without a third party app would be to change the default reminder time on your devices, but I'm still not sure how that'd translate to an event added from another device and then you'd have the weird 4 hours ahead of time reminder automatically setup on any new even created on that device.
Google Now notifies me of things like the Mrs.' work schedule when I wake up, but it always defaults to showing the weather in the notification panel and gives me the total number of cards it has to show me, so probably not the best for you.
When I first started using Samsung devices, the Samsung calendar would automatically create gmail alerts for me, which drove me nuts, but might be the easiest answer to your issue, assuming you keep up on your emails fairly well. If you can select for them to email you from the PC at a certain time for these events and you have that gmail address setup on all of your devices, you'll at least get that email no matter which device you're using.
Personally, I keep a full homescreen dedicated to my calendar widget. It's right next to my main home screen, so one swipe takes me to an agenda view of everything I've got going on for the next week or so, including things that she set up for us that I'm unaware of otherwise. (Whenever you tells me about something, my first question is always, "Did you put it in the calendar?")
Hopefully one of those option can help you out and get you the results you're looking for. As I said, I don't really want ever device I own to start ringing just because of one event, but I can see how it'd be quite handy to have the device you're currently looking at remind you of something without having to go in to each device and setup those reminders.
