If your 16 year old daughter is living with you and has started the licensing process, especially if she already holds a full driver's license, you need to inform your insurance company. Most insurance companies require you advise them of any licensed household members.
Your insurance company will normally require you to add your sixteen year old daughter to your policy however depending where she is in her licensing process they may allow you to wait to add her as an additional driver. For example if she has just started to drive and has a permit that requires a fully licensed driver to supervise at all times then some insurance companies will not require you to add your child at this time but will as they get their junior or full license.
Without knowing the specifics of your policy, especially the exclusions which can include not covering person under a certain age (i.e. under 21), we cannot tell you if your daughter would be covered to drive up to the store. You would need to speak to your agent and likely add your daughter to the policy so that she will be properly covered for driving any of the household cars.
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[Let CarInsurance.com help you find affordable auto insurance now.] If before you discuss the issue with your insurance company you let your teenage daughter drive to the store and she was in an accident you insurance company may or may not pay for any claims, depending upon state laws, the terms of your policy, etc. We have heard of some insurers that will pay out claims but then charge the parents for the premiums they should have been paying for the teenage child to be listed on the policy. | 
