Case::CaseID = CharacterRole::CaseID
Individuals::InvidudalID = CharacterRole::CaseID
A relationship can be added to link a case record to a specific role record by caseID and Role, but the resulting calculation will be unstored. Sorts and finds on such a field will be much slower than on a stored calculation. You may want to use a script to find and capture this data to put in a simple, indexed text field for you case name in order to get better performance.
That said, here's what you requested:
Define a calculation field in Case, constMother, and define it to return the text "Mother".
Make an extra occurrence of characterRole, MotherRole, and link it in a relationship like this:
Case::CaseID = MotherRole::CaseID AND
Case::constMother = MotherRole::Role
Make an extra occurrence of Individuals, MthIndividuals and link it in as:
MotherRole::IndividualID = MthIndividuals::IndividualID.
Now your calculation, defined in Case, can refer to a name field in MthIndividuals to return the name of the Mother in this case.