You seem to be talking about a phone rather than a Mac, is that right? If you're using a Mac, then everything is way easier, so you should check back. But the idea is the same.
Photos scans the pictures and records in its database the characteristics it finds in any faces it recognizes. Then, when you identify some of those faces, it figures out what they have in common, and it goes hunting for more like that. If it catches the wrong person, then you have to remove that person's characteristics from the recognition algorithm in the database. (I love that kind of talk!)
First, and this is important, add the Kid's name to the Caption field of every picture with the Kid in it. Then you should be able to find the kid with the search field rather than having to use a people album.
So go to, say, the MOM person album. Then go through every picture where Kid is miss IDed, or even correctly IDed, tap on the kid's circle, and choose "This is Not…". And do it again in the DAD album. Do this to every picture that has the Kid in it. You have to remove all those wrong characteristics. This will all be easier if you've put the Kid's name in the caption!
Then, since the caption hasn't changed, you can get all the (now non-IDed) Kid's pictures together and put in a new name. Just in case Photos is still confused, you should probably use a different name, like Kid2, or something. A few days later you can change them all at once in the Person Album.
This should work as long as the Kid is not too too close to MOM or DAD. Twins can be an insurmountable problem.
By the way, you should use the Cation trick with every person-- it's a more robust way to keep track of people, and unlike face names, the caption transfers with the picture. Also, you can put a name in a caption even if it's the back of their head!
Here is a discussion about face names, but it's mostly about Macs-- it will be good if you are really using a Mac, but you may find usable stuff for a phone. Macs can have keywords which are a bit better than captions.
Saving Face Names for Genealogy
Let us know how this works (or doesn't) for you…