First of all being a recruiter I can tell you that you are disqualified if you are a single parent. You may have to relinquesh ( think thats how you spell it) custody of your children. This may be differant for the Navy but it never hurts to ask I suppose. If you scored an 88 on the EST (thats what the Mock Test is called) Then you are project to score about that on the real ASVAB +\- 7-10 Points. Either way you are going to pass and do fairly well on it. Navy really likes to push that whole Nuke program becuase not too many people qualifiy for it becuase you have to almost be the perfect applicant.
Definitly ask them if being a single parent is a problem. Also don't let them talk you into taking a physical (MEPS) to "see" what you qualify for. Once you take the physical you are in the Navy or they will atleast do everything they can to get you to join right then and there. Me personaly I would never send anybody to physical who was on the fence and unsure about what he wanted to do. I respect you for wanting to serve your country and hope thats one of the main reasons you are doing this. Good luck to you and if you have any specific questions feel free to ask. try out this site as well.
http://usmilitary.about .com It might answer more questions than you might ever think to ask.