Children of record / divorced parents

i have found a lot of info on the forum, but have been unable to match this exact situation. i have also been unable to find it in the handbook. the handbook gives guidance on children that are already members, but not this:

biological father and mother share custody.
children spend majority of time with father and step mother. biological mother is a member, but does not attend church.
biological mother has legal residency custody of children.
children attend church with the father and step mother.
father and step mother are requesting children have membership records created, so they can be listed in the family and ward.
that's it. no baptism or any ordinances, just a membership record. is this doable?

thanks,

gt schulz

33.6.2: Members of Record

The following individuals are members of record and should have a membership record:

Unblessed children under age 9 when both of the following apply:

• At least one parent or one grandparent is a member of the Church.
• Both parents give permission for a record to be created. (If only one parent has legal custody of the child, the permission of that parent is sufficient.)

The way I read it, you need the mother's permission.

thanks!