MS Access Many-Many Query/Form Assistance
I'm having to do a little bit of psychic debugging here, but generally speaking, you should have the subform bound to a query that joins your junction table to the table of related records. The form inside the subform shouldn't know about the table in the left side of the relationship (tbl_apptltrs).

So the chain is something like this:


Main form bound to tbl_apptltrs.
Subform linked to main form via primary key of tbl_appltrs (e.g. parent form ApptLtrsID = subform LinkedApptLettersID).
Form inside subform bound to query that joins jtbl_apptltrs_mbrs to tbl_mbrs (jtbl_apptltrs_mbrs.LinkedMemberID = tbl_mbrs.MemberID).