Air force question about get out of DEP?

im suppose to leave for basic october 14, recently my mom has had some medical problems and she a single mom and im her only child. i feel that i need to stay and give her support. i called the recruiter couple days ago cause i wanted out because i wanted to join the army, then about a day or 2 my moms problem came up. The shouldn't give me a hard time getting out right? If they do im still not going to show up my mother is much more important then them