No way! Caroline has always been a steady name. It's recognised as being one of the most consistent favorite names ever! Yet, it has never being an obnoxiously popular name. Caroline is a smooth, steady, classic. Most of all it's very humble.
No. Isabella (being an obnoxiously popular name) seems like a failed attempt at someone tying too hard to pair the *right* name with Caroline. Caroline and Norah, Caroline and Simone, Caroline and Annabel, Caroline and Diana... a name along those lines would be perfect.
Isabella Caroline does not flow, at all. Caroline Bella or Caroline Isabel would be more suitable.