I did about 2 years at sbcc then transferred to ucsb for chemical engineering and i am from Santa Barbara (so possibly a little biased). Look at assist.org if you haven’t already for articulation agreements from sbcc to ucsb. When i transferred they had a tag agreement for engineering but they don’t anymore which makes admissions competative, so you want to shoot for a 4.0 college GPA when u apply to transfer which is NOT easy. High school stuff will not matter for transferring. Sbcc science and math classes are top notch and challenging. Professors are very good and focus only on teaching, not research which makes the classes very good. i was very prepared for upper division at ucsb and felt that math classes at sbcc prepared me better than my fellow students who took their lower div math at UCSB. A down side of sbcc is you really gotta fight for class spots, as soon as registration opens u better have your schedule planned and ready to fill.
If you are procrastinating now you need to change that. All engineering classes get very time consuming and challenging make a commitment to never leave a final exam thinking you could have done better in the class. At ucsb taking weekends off was often not an option to get an A in some classes and sometimes i still got a B+. If you go to sbcc, don’t think it will be just a cake walk and then transfer with a 3.6 GPA, u probably won’t get in with a 3.6. There is a big party scene in SB that can drag you down, it’s ok to have fun but, stay focused if your dream school is UCSB.
I have a job now and my employer did not care i was a transfer student, they cared about my UCSB GPA (i got a 3.8, the highest GPA in my class was a 3.92), experience in the field, (research, internships, etc) and communication during the interview. For engineering i don’t think school “prestige” has a big impact like your parents are worried about, although UCSB does have a stellar engineering program.
I love sbcc i love UCSB i recommend that option if you are ready to work your ass off. Otherwise take one of the options where you are already admitted to EE, DO NOT go to a school where u are not already admitted to the engineering program from the start i have heard several horror stories. i don’t know out of state tuition or anything but i think u still save alot of coin doing the cc transfer route. MAKE IT HAPPEN! Good luck!