I went to Caltech for undergrad and had a great experience. The courses were hard, but the school funneled a lot of resources into helping students get through them to minimize the number who fell through the cracks. It wasn't a meat-grinder like (I've heard but don't know first-hand) some places are.
Regardless of which school you go to they probably have programs to help you when you're struggling - be sure to look for them! Engineering school is hard, but if you can pass your classes, line up interesting co-ops or internships, graduate, and land your first job, then Engineering is a fun and lucrative profession.
Another thing to consider is that you'll want to balance your hands-on training (which FRC is great for) with your heavy-duty analysis training. Caltech went a little overboard on the analysis in my opinion, but their Mechanical Engineering department does have a hands-on
FIRST-like competition every year for undergrads. You'll have far better job options in the working world if you're strong in both theory & practice.