Midgardsormr says it's one of his kids, and then we're told it's one of the Great Wyrms (Wyrm Kings) of Eorzea, so we know from that that his child is a wyrm king and a great wyrm, and is the one who called the attack on Ishgard. It's also likely, given the lre of Nidhogg, that it's Nidhogg who is the one leading the attack, and therefor Nidhogg would be the child of Midgardsormr.