The mom is a princess from the foreign nation looking for ice mage lady-in-waitings. They're looking for her daughter (because theoretically either ice magic and girls run in the family, they ran away after she was born and they somehow found out, or a mix between the two) so they can find the rest of her family. I can't wait for her to become a princess and have a good enough social status to marry Lockman, a future Duke. Lol the anticipation is killing me.