Welcome! This forum has a treasure trove of great info – Scouters helping Scouters! Just a heads up, though - all content, information, and opinions shared on this forum are those of the author, not the BSA.
My recommendation is to have parents create an account at my.scouting (if they do not already have one). Many parents already have a BSA member ID number and just need to connect to it when creating a my.scouting account.
When units create a Scoutbook account for parents, what usually happens is that the Scoutbook account gets created without a date of birth (DOB), which is one of the ways that duplicate / multiple BSA member numbers get created.
Parents should use their full legal name when creating an account – not a nickname. This will also reduce the odds of duplicate / multiple BSA member numbers being created.
It appears the mother is already connected to this Scout account and she has a my.scouting username. She just needs to log into Scoutbook with here existing username
The issue I fear is she will not remember her password and without an email on file she will not be able to click “forget password”
Can you tell me if the two accounts she has is one of them firstnamelastname[3DIGITS]@someplace.com and the other(which she should use) is just firstnamelastname[3DIGITS] ?