@rcooper6,
Let's make sure you understand the distinction between the beneficiary of a life policy and the owner of a life policy. The owner is the person who pays the premiums. The beneficiary is the person who gets the money once the person designated in the policy dies. The owner and the beneficiary can be the same person, but not necessarily.
It sounds like your mother was the owner of the policies that she took out on you and your siblings. It also sounds like she was the beneficiary. Now, here's the first problem: once she died, the policies, because they apparently were whole life and thus had a cash value, should have become part of her estate. In other words, those policies should have been distributed to her heirs according to the laws of intestate succession (since, as you mentioned, she didn't leave a will). The question then arises: how did your sister end up with the policies? Was that part of the estate that she inherited? Or did she just end up with them because nobody was really paying attention?
Second problem: your mother had what is called an "insurable interest" in the lives of her children. Having an "insurable interest" means that a person would suffer some kind of pecuniary loss in the event of the insured's death. A parent has a presumptive insurable interest in her children, just as a husband has a presumptive insurable interest in his wife (and vice versa). A mother, then, doesn't have to prove that she'll suffer a pecuniary loss on the death of one of her children, it's just assumed. A sibling, on the other hand, doesn't have a presumptive insurable interest in the life of another sibling. Your sister, in other words, would have to prove to the insurance company that she would suffer an actual financial loss on your death. Otherwise, the policy is a "gambling policy" and would be void as contrary to the public interest.
If your sister became the owner and beneficiary of those policies, I don't see why the insurance company issued (or converted) those policies in the first place. It shouldn't have issued a policy to a sister on the life of her brother unless she could show that she would suffer some kind of financial loss in the event of your death. That fact makes me suspect either that something is wrong with the policies (e.g. maybe a misrepresentation in the application) or else the policies no longer exist (i.e. that the insurance company paid off the cash value of the policies when it became aware of your mother's death, and your sister just took the money for herself).
But let's imagine that nothing is wrong with the policies, that your sister is legitimately the owner and beneficiary of them, and that they really do exist. Do you have the right to cash them in?
No.
As I understand it, you're just the insured. You're not the owner. Consequently, you have no rights in the policy. Only the owner can cash in a whole life policy. If that's your sister, then she has every right to refuse your request to cash in the policy and give you the money. Now, it's possible your mother wanted you to be able to cash in those policies and receive the cash value at some point. If that was her wish, then she should have written it out in a will. She didn't. That's too bad, but then that's your tough luck. Don't make the same mistake yourself -- make a will.
EDIT: I skipped over the entire second page of this discussion, so I missed the fact that
Dadpad and
engineer already addressed the estate aspect of this matter. My apologies to them. I didn't mean to step on your toes.