According to the State of Washington Department of Licensing when you drive in Washington, you must have insurance. If you drive a vehicle that is registered in Washington, or one that is required to be registered under the Revised Code of Washington (RCW) 46.16, you must have financial responsibility for the vehicle. Most people do this with auto insurance. If you choose to have auto insurance the limits must be at least:

• $25,000 of bodily injury or death of one person in any one accident.
• $50,000 of bodily injury or death of any two persons in any one accident.
• $10,000 of injury to or destruction of property of others in any one accident.

What is helpful to your current situation is that Missouri also has minimum liability requirements of 25/50/10. However since you have moved away from your mother's household and registered the car in a different state it is unlikely that her insurance company will want to continue to cover your vehicle under her policy.

Generally if your vehicle is garaged a majority of the year in a different state the insurance carrier will require you to now insure in that state. You and your mother should speak to her insurance company to see if they will allow you and your vehicle to remain on her policy or not. They need to be informed of your move because if not and you are in an accident they may be able to deny a claim due to you not advising them of changing states and registering the car in WA.

If your mother's insurance company does business in WA as well as MO then they may be able to help you transfer your car from your mother's policy onto your own Washington State insurance policy.

Otherwise you will likely need to shop around for Washington car insurance to find affordable auto insurance.