my own experience. my father-in-low came to the States with a one year multi-entry visa. He got a 6 month stamp but wanted to stay another 6 month. So I took him to Tijuna, Mexico for a new I-94. We went there one month before his I-94 expires. We were told he can't get a new I-94 unless the current one is expired or expiring. a.k.a, Applying for a new I-94 several days earlier than the expiration date is acceptable. But not earlier.
He applied for extension anyway in the end. And notice that you donot get any decision regarding the application coz it takes 3 months to process it now.
Good luck to your family.