Integrated math 1/2/3 to cover the content traditionally covered in algebra 1, geometry, and algebra 2 is not a Common Core feature. Before Common Core, some California high schools used integrated math 1/2/3 while others used the more traditional math courses. This appears to be the same after Common Core.
Both UC and CSU accept either sequence for the minimum math requirements (see https://hs-articulation.ucop.edu/agcourselist#/list/search/all ), but students intending to go on the UC, CSU, or other selective colleges ought to complete higher levels of math (i.e. precalculus/trigonometry following the completion of either of the above sequences; calculus recommended if precalculus/trigonometry is completed before 12th grade).
Why does she want to attend a large out-of-state public schools instead of a UC or CSU which would likely cost less? Is your financial plan in place to afford out-of-state public schools?