Can I do something when a car struck me and my girls without insurance but the other driver did?

You can get reimbursed for your out-of-pocket expenses, but not for pain and suffering (Ca Civil Code 3333.4). Your girls have good claims.

Check with your own insurance carrier; most have a provision that they provide insurance coverage for the first thirty days on a car you have just purchased. If there is no coverage, you, as the driver of the vehicle, can not collect for any pain and suffering, but all the passengers in your car can. You still can claim out of pocket expenses such as vehicle repair and rental, medical bills, wage loss, etc.