There shouldn’t be a problem logging on to your account from your parent’s laptop. However, you need to be sure that no one else is using this laptop or your internet connection to sell on Amazon. As another seller mentioned, it would be a good idea to be proactive and e-mail Seller Performance for more information.

https://sellercentral.amazon.com/forums/t/can-i-use-another-laptop-to-login-my-amazon-account/179939