What military service is best for a mother of 2 small children?

I have two small children 19mnths & 3mnths. I'm technically single bec I'm not married but I'm still with their father. I really want to make a change & provide a good stable life for them & I feel like serving my country at the same time is the best way to go. I've always wanted to join the military but in 2008 I got pregnant & shortly after having my son I got pregnant with my daughter so now is the time that I really wanna weigh all my options. I'm 21 years old & have always been very athletic. We've talked about getting married but I don't want the military to be the sole reason we do. Either by getting married or signing away my rights to their father, what service do you think would be best so that I can spend as much possible time with my children. I know no exceptions are made for parents & I don't expect that either. I'm leaning towards the Air Force. I graduated high school & have 12 college credits.. If that matters. I'd love to hear many opinions if possible. I'm doing this for my children so I don't have to ever rely on someone. I wish I could say I feel like me & their father will last forever but I have my doubts. Is it possible to fight for my rights back if I sign them over? Thank you.