Dunno what grandpa's worries about, Dou will become the greatest demon lord ever.
She is literally invincible: everything that has ever meant her any harm has immediately become her friend before being able to even scratch her. The universe will simply not allow any malice towards her to exist.
The demon kingdom would be safe from all threats: nobody wants to declare war on her and make her cry because you said you hate her. Anyone cruel enough to do so anyways would immediately be swarmed by the rest of the world as every nation tries to make Dou feel better. She'll probably form a global alliance when she asks everybody to be her friend.
She has the power to put a stop to a war that's existed forever by uniting heaven and hell: right now the angels and demons aren't actively fighting but hostilities aren't completely gone. They won't start fighting again any time soon thanks to her 2nd superpower, but she also has an angel crushing on her hard, and he promised to be the king of heaven someday (which might not be an exaggeration since the angles called him "Mayuu-sama" so he's somewhat important)
Forget world peace, Dou will bring universal peace.