You may want to get an actual number on that “strong possibility” of your extended family “pitch[ing] in”. They may be willing to pitch in, but the amount they were thinking of may not be as much as you think, since they may not realize what college costs these days.
There are 21 schools with bachelor’s in nuclear engineering programs. University of Florida is the only in-state public one for you. Most of the rest are out-of-state publics, typically with high prices and no or little financial aid for out-of-state students, but some have large merit scholarships. Two are private (MIT and RPI), and one is the USMA (for those who want to become Army officers). See http://main.abet.org/aps/AccreditedProgramSearch.aspx/AccreditationSearch.aspx
For chemical engineering, your choices are much wider. If you are unable to get clarity on family contributions, http://automaticfulltuition.yolasite.com/ lists a number of big scholarship safeties for your stats:
Alabama
Alabama - Huntsville
Tuskegee
Howard
Florida A&M
Louisiana Tech