You will not be able to work full time and attend Med school. The curriculum is just too demanding. Med school is set up so that it becomes your daily 9-5 (actually more hours than that). As far as you not getting in the first time around, that depends on your science GPA, MCAT score, apps/interview skills and some other factors.
Now for the question about kids in school. To answer your question in short, yes I think it can be done. I think the real issue to ponder is whether or not this is something you can handle. You will be sacrificing seeing and being with your kids more than most single moms. And the pressure of not having the extra support may be emotionally and financially burdensome. Medical school already adds such a large emotional and financial burden that this may not be something you want to put you or your kids through. I know single moms at my Med school. But I believe most of them have only 1 kid and they have family that will help in some way.
As an MD3, knowing what I know now about Med school, I personally would not raise 2 kids alone while in school. the time is simply not there to do it and the sacrifices for my kids would be too great. After taking in everyone’s advice, this is a decision you need to be at peace with within yourself. Because when things get hard (and they will) you have to KNOW that you made the right decision for your family.