Unless your family donated enough money to fund a building in their name, this isn’t going to help you gain admission OR get more financial aid.
Legacy status also isn’t going to get you more aid.
Tulane does not guarantee to meet full need for all.
A safety is a school where your admission is pretty much a shoe in…and the school has a reasonable way of being affordable.
In my opinion, neither of these schools would be a safety for you.