Single mother...How can I join the Army?

You will just have to do what they tell you to do even if it takes longer. I know it isn't what you want to hear but the army does this because some single parents (not just women) used their kids as a way to get out when they didn't want to deploy or simply didn't want to serve anymore. The army wants you to prove to them that you won't be one of those soldiers when your unit gets orders to deploy. Get with your recruiter and he should be helping you along the way but you can also try to get advice from a lawyer as well.