SQL CPU trigger on machine memory load
It sounds like your machine is memory starved.  If your app uses a lot of memory and there are two sql instances, one standard and one express, with the default max memory setting if 2 tb, you're probably seeing the sql process cpu spikes as sql's memory is being paged out or returned to the os.  You should set you max and min memory for each instance based on the workload, and also set the maximum memory your application will use if possible.  That way you can ensure all three applications plus the Os have enough memory to coexist.