Welcome to Just Answer. I am here to help you resolve your tax and finance concerns. Please feel free to ask anytime you need extra help.
Filing separate tax returns will not change anything. FAFSA will still look at the incomes of both parents. Listing only one parent's income is fraudulent and will be detected since the FAFSA processing center verifies all data with the IRS. This will cause a complete denial of assistance and could create other, even worse, issues - criminal attempt to defraud. I would not advise doing this.