OP, you are right in thinking this will take much reflection and consideration. Accordingly, I will attempt to categorically segregate the different concerns for your situation. Warning: this will be a long post.
I am not aware of a 5-year policy for how old pre-req courses can be, but if you are missing any at all, definitely find a way to complete these before applying. Non-degree seeking or post-bacc programs in your area may be something you need to consider. Also, if you plan on applying DO, retaking courses will be a wise decision because of their grade replacement policy. You could really bolster your app for DO schools this way. MD schools don't offer grade replacement, so I'm not knowledgeable on how attainable an MD/PhD acceptance would be. I would encourage you to research more into requirements for MD/PhD.
How much do you have? If you're lacking, get crackin'. Hospital volunteering, shadowing, non-medical stuff. Definitely shadowing. I understand this may be difficult given that you are a single mother. Try your best to accomplish this if you don't have as much clinical experience.
Although I have to admit your undergrad GPA is more in line with pursuing the DO route, there is also the downside of not being able to get a PhD (at a DO school) in a field pertinent to your ultimate goal of oncology research. A lot of DO schools are unfortunately severely limited in research opportunities and may only offer PhDs in Health Policy or something of the sort (not very applicable for oncology research). One school that sticks out to me is Michigan State, because I know MSU has a lot more research opportunities due to the fact that they also have an MD program. I was considering MSU's dual program because of their pharmacology and toxicology track (http://www.com.msu.edu/research/PhD-Admissions.html
). According to MSU's DO/PhD website, your GRE is average (MSU: 580 Verbal, 720 Quantitative). Their website also states that the avg MCAT is 29-32, so you need to make sure you hit this mark. Study hard.
I have a background in pharmacology and am also looking to pursue research residencies and fellowships after medical school. However, I'm not too sure how necessary a PhD is for oncology research. I guess it depends on whether you are interested in translational research. That is, bench-to-bedside type of research. In this case, I would unequivocally say that a laboratory PhD would help tremendously. There is a researcher that works next to me that has a MD/PhD and does animal model studies as well as clinical trials, so clearly a PhD is helpful/?needed? in his case. However, if you are more interested in doing clinical research with anti-cancer drugs, then I would say that a PhD is probably not worth it, as you don't need
a PhD to do clinical trial research if you already have a medical degree.
Since you haven't taken the MCAT yet, I agree with another poster in that it may pose as a problem. It would probably be wise to retake some courses for preparation. If you feel that you don't have to/are unable to do so, then you may also consider enrolling in a prep course (class or online) or allot 2+ months of solid MCAT prep (there are some excellent threads on MCAT-prep).
You mentioned having a good financial support from your family. This sounds important to you and it should be considering the financial sacrifice of going to medical school for 4 years and 5-6+ years for residency and fellowship training. Pursuing a PhD while in medical school will help reduce the financial burden as there is usually tuition compensation for research involvement.
I would suggest not pursuing the PhD at this time and put intense focus on preparing to apply to medical schools. Retaking courses via non-degree seeking/post-bacc would take a year of an intense course-load, depending on how many you need to retake. Attending a Special Master's Program (Georgetown, UCinnci, BostonU, etc.) would help make you a more attractive applicant for MD schools, in particular. So you're looking at 1-2 years there. I know I mentioned DO a lot in this response, and I apologize if that bothers you. But as it stands, I agree with another poster that your GPA is more in line with this route. If you retake courses and do well, then there's nothing stopping you from applying broadly to MD and DO schools. I would encourage you to do so.
I've been going at this for a while now, so if anything else pops into my head I will edit to add, but I hope this has been helpful for your planning phase. Phew, that is all for now. Good luck, though! You can do it!