When adding another vehicle to your policy, your price will likely increase. Though some companies offer discounts for having multiple cars on your policy, you are still adding additional coverage to your policy. For example, if your mom needs full coverage on her vehicle but you have liability only, your rate is going to increase.
However, since your mom is already rated on the policy as a driver, you ideally shouldn’t see a large price jump.
Doing this will allow you to see what companies can offer you the best rate for multiple cars and drivers, along with the specific coverage you need.