Aluminium zirconium trichlorohydrex gly has long been the active ingredient in most antipersirants. It's also a cool weird to randomly through out when it's not even relevant, just to be weird.
The FDA is pretty picky in my opinion, so I figure they'd be on it if it were a real concern. Regardless, sometimes it's best to humor the inlaws and let your spouse talk to her own parents if and when something needs to be addressed.