You have to provide the cruise lines (not just Disney) with each passenger's date of birth. Further, you'll be presenting a passport or birth certificate before boarding, so that kinda puts an end to fibbing.
Having a teen's correct age has some real benefits for all. For example, under 18s are not allowed off the ship in ports without adult approval (the key card is swiped and the associated computer record checked before every passenger is allowed to disembark). I'll presume most parents are happy to have that safeguard in place. Age is also needed for access to the spa and fitness center - I'm sure it has something to do with possible legal troubles if adults touch underaged persons during a spa treatment, and the legal validity of the waiver forms all shipboard spas require of their patrons for hands-on treatments.
On the other hand, the teen program on board is off-limits to 18 year-olds, so if you did successfully fake her 18, she'd miss-out on a whole lot of activities.
All that said, the only time it's likely that a 17.75 year-old will have his/her ID checked at the adult pool is if she's misbehaving/disturbing other passengers.
As to Palo, your neice may prefer to dine with the rest of the family, but she might also have made friends on the cruise in the teen program and take that opportunity to hang out with them instead... adults' night out = teen's night out.
Co-Author, PassPorter's Walt Disney World, PassPorter's Disney Cruise Line, and PassPorter's Disneyland and Southern California Attractions