A good law school? Don't go to a online university then.
University of Phoenix is accepted by the LSDAS, but the good law schools won't consider you.
There are some regular universities that have online schools, but I believe you have to be admitted in to their regular school before you can take online courses for a degree.
Law schools don't care what major you are. Literally. You can have a BA in basket weaving for all they care. The idea is to stand out to the good law schools. Poly sci is NOT the way to do it. They have plenty of poly sci applicants. They know that major is easy, so you'd better have great grades if you're a poly sci major. Same with online. Law schools know online schools don't exactly have the greatest rep. So, you're facing an uphill struggle already.
If you need to ease back into school, I'd take courses at a JC. Then transfer to a regular 4 yr university. The better the law school you get into, the easier it is to find a job.
You can be a lawyer by going to a non-ABA law school, but it's not easy. They have poor bar passage rates and employers look at you last (if at all).