If the child is applying now, isn’t it already too late? The time spent is the 365 days before the date of filing, isn’t it? Unless the child takes a gap year, I don’t think it matters.
Under no circumstances would I hand an ex- any personal paperwork, especially a tax return. You’d have no way of knowing whether or not he created a FAFSA ID in your name and used your info. to fill it out. Claiming the children live with you more when they don’t is fraudulent. If that happened and it was discovered, I think you’d be liable for it. That means (at the very least) that you’d have to pay back any financial aid your children receive.
The way circumstances are now, he’s responsible for filling out the FAFSA with his data. At CSS profile schools, you’ll submit your part of the app directly to the school, so there’s no need for your ex to have any of your financial info. To get an estimate of what a college might cost, suggest your ex run each college’s Net Price Calculator with his info. You can run it separately with yours and add the totals together. If his income is high, just running them with his will give him an estimate of the minimum each college will cost.
Make sure your children give you access to their portals so you can keep an eye on finances. You’re responsible for any info. filed under your ID, so make sure you keep track of it.