Well, barring some miracle in dealing with the insurance company the policy w/out a beneficiary designation will be paid to her estate. So you will have ot set up an estate and distribute the policy either under her will (if she had one) or under the laws of intestacy - if there is no spouse it would likely go to the children.
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Depending on the value of the policy, you might be able to present the insurance company with an affidavit for collection of personal property or similar affidavit available for small estates. Ask the insurance company in advance if they will accept this. If not, you will need to open probate.
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the assets would be payable to the estate. There should be a "short cut" way to open a small estate in Virginia. The proceeds of the policy would be subject to the claims of creditors since the policy is an estate asset. Depending on the value of the policy, I have had clients who decided it was not worth it to open an estate and did not redeem the policy.