I think your odds for Vandy and Rice are just as tough as they are for everyone else. BUT, I would not let your situation from freshman year stop you from applying. I actually think it makes you a somewhat interesting applicant and says a little about your character. I’d be sure to ask your counselor to explain the situation well in his or her recommendation letter.
My daughter goes to Rice and while it’s a tough admit they seem to like somewhat unique stories. They are also very big on their “Culture of Care” (https://admission.rice.edu/life-rice/community). It’s a real thing at Rice and I think you helping out your relative says a lot about you and that perhaps you’d fit well into their culture as well.