First of all, bless you for your heavy burden of working and raising two children with no help form their father. This is an extremely difficult situation, and everyone pays the price. As a mother, you have to take total responsibility for your children (which you are), and with no help, it is even harder than in a supportive situation with two solid parents. Your time spent working adds to the stress for you and your children. You are not a failure!!!
It is possible, that your daughter has a disorder, but blow ups are not a way to tell. Since she got to that point after being bossy, whiny etc, it sounds like a natural next progression is to escalate to blow ups.
A doctor told my friend to rule out ADHD until a child lives for a solid year with a wholesome diet, enough sleep, total support and love, firm structure and rule enforcement, and after that, if no matter how much support is there, the child can NEVER hold their attention, and their behavior is out of control, then to test for ADHD. She changed a lot of environmental aspects of their home, quit her job and got her husband to step up and not be "the nice guy all the time"(not an option for you I know) and all three of the kids improved drastically in just a short time. before that, she thought they all had ADHD, ADD or ODD or Aspbergers or shrunken frontal lobes etc etc etc.
Outbursts can be a symptom of these disorders, but they do not mean your child has these disorders. They might, but it sounds like they have many other things putting a strain on them too. You don't want to label your kids with a defect, and then focus on that as the cause of your problems, because the way you handle the situation will be based on their "genetic flaws" instead of what you can do, and you're the mama! No one knows the long term health effects of medicating young children, so you want to use that as a very very very last resort.
I hope you can find a way, in your hard circumstances, to give your children more time, more love, more discipline, and more support as well as find out if there is ADHD in the picture. I hope you get lots of good tips. A strong male figure is very important for your son especially, if you can find a coach or some activity where he is around a strong male-a trustworthy relative etc who holds him accountable for behavior and gives him responsibilities to be proud of. You are in my thoughts, I hope you all the very best. I hope your daughter is strong willed, healthy, and ADHD free, and your future is bright. When you do meet a daddy-to-be, make sure he's a good man!