the plastic cap? or just the socket part of it?
if that's broke, it may be a case of smash with a hammer/screwdriver ...but not until you get a new cap... a salvage yard may have one off a Sonic, Buick Encore or Cruze...
Looking at your new cap is the thread and housing below the top of the cap? At this point I'd say drill a hole on the side as close to the top as you can and use it to turn the cap off.
I'm quit concerned my dealer torqued it on like this..just like my oil pan bolt...
Damn...
The only thing I can think of is to try to break the edge (threads). I can see the filter underneath it probably not helping stuff to move. And you're right, it's not easy to get in there... Perhaps a long screwdriver could come up enough from the engine area to allow some good hammer hits on that threaded area...If it could be pushed a little it may be able to be unscrewed by hand.
Do you have a replacement?
I always use Mechanix gloves. I can't wait to get it off so I can get to worksome of those mechanix gloves might also give you a little more grip than an oily hand..
Reminds me of me and my Dad, years ago, couldn't get the filter off the Nissan pickup he had. When we did get it off, we beat the **** out of it with an axe! (the filter that is)... felt good to get the rage out!
I will keep doing that, from the pictures there is not much room to work. The angle sucks where it is at.Wouldn't cut it, you will get abrasive particles in the oil.
I'd get a good sharp chisel and start chipping away at it. I had to do this on a cadillac CTS with the 3.6L v6, has almost the same cap as us but metal. The nut broke off, and I had to knock the old one loose like that. It will move eventually, as you break it apart it will hold less and less tension.
heat up the cap with a hair dryer while the engine is cold hope fully the cap will expand enough to loosen off for you