Maybe I can help? Did you read the iPhone Manual? Always RTFM first. I've read lots of whiny posts that iOS devices aren't pushing or synching - the Manual states that "push" for iCloud works on WiFi only, defaulting to the Fetch schedule, so also check your devices' Fetch schedule (mine are set to 15 minutes; I actually set my devices to Push but override the iCloud accounts to Fetch at 15 minutes to reconcile my mail/calendars/contacts without having to open the apps).
If you're only any network, iCloud calendar changes aren't necessarily synched in a timely fashion with most CalDAV servers set to a minimum for polling of 15 minutes - so a change on one device can happen in up to 15 minutes to the iCloud server and another 15 minutes down to your second device. If you're just going to sit there and watch you're going to be disappointed - and the Manual also states that refreshing the Calendar app is accomplished by closing and reopening the app. Using Calvetica isn't going to change this - that app (which I also use) is just a skin or shell of the Calendar database and Calendar app.
As soon as I took the time to learn the benefits and limitations of CalDAV and what "push" really means (which are published on Wikipedia), I got to stop whining about my iOS devices and get on with it.
I use a Mac, which uses a sync engine called Syncrospector, and iOS has a similar sync engine - they're apps, and they hang sometimes. I generally reboot my device once daily, after an app installation, and if I feel something's "sticking". Regardless of what people want, smartphones need to be rebooted - I've read through a Console file in an app that reads what's going on in and iOS device, and there's a lot of services that don't start up when they ought to. So, consider rebooting your devices, and while you're waiting feel free to RTF(rick in)M. And, understand there might be a provider or iCloud data interruption - VZW has had lots of hiccups in their data network lately; if you're a Windows PC user, recall how finicky XP can get when a network is down and apply that understanding to your nifty new smartphone and iPad.