Hello,
I stumbled upon this topic because I had exactly the same problem with exactly the same phone and version of Android. I also have Galaxy S2+ with Android 4.2.2 (automatically upgraded maybe a week ago) and until today I've experienced absolutely the same problem with android.process.acore & com.android.providers.applications, problems that started maybe a day or two after my phone downloaded and installed 4.2.2.
My battery was being drained in a matter of hours, "something" consumed 10 or even 15% per hour (7% if I was extremely lucky) without me doing anything... literally anything. Situation was the same with WiFI, Mobile Internet and GPS turned off.
Watchdog Lite reported that "Android Core (Homescreen)" used at least 40-45% of CPU all the time but it wasn't really detailed and I couldn't do anything. Have been searching the net for hours in hope for solution without success.
Then I installed Android System Info and it told me problem was "android.process.acore" with package: "com.android.providers.application", Status: "Foreground", User ID: "10007".
What I did next is to switch to Apps tab of Android System Info and look up for an application with 10007 ID.
Turned out it was
CONTACT STORAGE. Immediately after I cleared its cache and data all problems stopped (
WARNING: Clearing data will remove all contacts from your device. Back them up to SD card, Google/Samsung servers or maybe SIM card if possible and just import them back again - it won't make heavy CPU usage again. and haven't reappeared yet. CPU can have a break now

and battery is losing only 1-2% in idle state, which is fine I believe, especially compared to 10-15% per hour.