Since the car is kept at your home, you would need to insure the car in your name and address. You will also need to list your mother as a driver on the policy since she is the owner, and as an additional interest on the policy since she has a financial claim to the car.
If your sister is the policyholder, you will have to have her call her insurance company to access the policy information. Since the car is registered in your name, the insurance either needs to be in your name or you need to be listed on her policy as an additional interest.
As long as your husband is going to drive the vehicle and park it as his residence, he can insure your car under his name and policy. Because you own it, you would need to be listed as an additional interest in the policy.
You can get insurance in your name but your girlfriend will need to be listed on the policy since the car is in her name and she will be driving the vehicle. If you have any further questions, don't hesitate to ask.
If you have a Named Driver policy, that means the people listed as drivers on the policy are the only ones covered. Since the driver is not listed on the policy, they are not covered to drive the car and the insurance company can deny the claim.