I’m applying to transfer to a UC for the fall of 2016 and I am unsure if I can exclude a couple classes I took in the summer vacation of my sophomore year in high school.
No, you need to include all courses.
As usual, @guineagirl96 is correct. All college classes taken in HS must be included.
You need to send official transcripts for all college-level, credit-bearing courses.
Yes, you have to report all courses/grades, BUT if the courses are not UC transferable (which is entirely possible, I took a non-transferable algebra course to fulfill a HS requirement during my sophomore year of HS), it won’t be factored into your GPA or counted towards your total units.