The answer is YES. The insurance carrier may exclude a family member from policy coverage based upon various things which they believe might increase the risk of additional claims -- multiple collisions are among these events. You should immediately A) consult with an attorney, B) enroll in a (another) driver education / remediation program, and C) have/allow/ask your parents to help you find a good place to start doing some type of community service. ALL OF THIS should be started promptly, before any notice of a hearing, and well before going in to court or a hearing. You want to have certain things in place to make sure that you do not inadvertently HELP the insurance carrier remove you from coverage.
Yes, it is possible that the insurance company may seek to drop you from coverage or increase your parent's insurance premium the next time it comes up for renewal.
You should not be discouraged, because you are young and learning and hopefully have learned from your recent errors. I suggest that you fight the ticket you were issued, as it is possible that the witnesses may not show up or the officer may not appear or be able to testify, if he was not an eyewitness to the incident. The officer can only testify to his observations and things that you may have said to him at the scene. He cannot repeat things said to him by others (hearsay).
If you are able to defeat the ticket, you will avoid additional points on your license.
If your parent's insurance company takes adverse action against you, your parents should consult with an independent insurance agent and shop around for insurance that will protect you as well as them. Under no circumstances should you drive without liability coverage.
Legal Disclaimer :
Mr. Lundeen is licensed to practice law in Florida and Vermont. The response herein is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter within the question. Oftentimes the question does not include significant and important facts and timelines that, if known, could significantly change the reply and make it unsuitable. Mr. Lundeen strongly advises the questioner to confer with an attorney in your state in order to ensure proper advice is received.
Mr. Flick gave you some very valuble advice. I would add to avoid making public statements such as "My fault-". I'm SURE you meant to state only that you were cited at the scene of the accident.
Do contest the ticket and if you must plead to the ticket plead no contest as that is no an admission of liability to any injured parties. Also if you have an insurance agent do speak to him or her.