Do grandchildren whose mother passed away during their grandfather's lifetime inherit from him in Islamic Sharia, knowing that the law and custom in the country they live in dictate their inheritance?

If the legal heirs are adult and of sound mind, and they agree to include a person who is not legally entitled to inheritance, by way of waiving a portion of their right, then there is no harm in that. This waiver must be with their complete consent. It is not permissible to rely on custom or state law if it contradicts Islamic Sharia.