Part Member family - non baptised youth

We have a part member family in our ward, in which the mother is a faithful member. The father is a non-member but is supportive and comes about once a month and comes to activities. They have requested to have the family members show up on the church rolls etc.
The oldest son is 8, but has not been baptized, and his name has dropped off the rolls. This is an issue as he isn't showing up in class lists etc. I have had multiple requests from the primary presidency, teachers, and the family themselves to get him added back in. When they approached me I teased them that they needed to just all get baptized, and they are likely headed in that direction - he has a sister who is turning 8 and wants to be baptized. There doesn't seem to be anyway to get non-baptized youth from part member families to show up in LCR/MLS. I think it is a great idea to have them drop off automatically when they turn 8, and maybe again when they turn 12 and 18, but it would be nice to be able to add them back in if they and their family desires it.

I'm a bit puzzled by what you describe. There used to be two ways a unbaptized child could show up on rolls in MLS. They could be a 'Child-of-record' which means they have a full membership record which was created before they turned 8. Of they could have a non-member record. 'Child-of-record' records never go away automatically. Once the child turns 18 and haven't been baptized the bishop (with consultation with the stake president) can decide to cancel the record but it has to be done manually. Nothing happens to a 'child-of-record' record when they turn 8.

If it was a non-member record then it would have disappeared because the church recently removed the ability to have non-member records in MLS. But if the children had non-member records then all of the children should have disappeared when all non-member records were removed. The only way I can see for the 8 year old to disappear and not the other children is if he had a non-member record and the other children have full records.

In any case, once a child turns 8 there is no way to create a record for them except for them to be baptized. For children under 8, with the permission of the parents, you can create records for them.

Given that non-member records used to exist and have been removed, I don't think they will be coming back. I assume there were legal reasons why they were removed.

So it looks like we missed up and didn't make the child a child of record when we should have. He wasn't born in the covenant as his parents aren't sealed. How can I go back and fix this now, or make sure I have the other children correctly recorded as children of record?

You can't do anything about the child who has turned 8 (except for baptism of course). For the other children you can look at the Member List in LCR or use the Membership > Individual Record menu option in MLS to look for a record for each one. If you find one then they are children of record. If not, you can create the records using the Membership > Ordinances > New Child of Record menu option.