If you look again at the 1881 although Frances Saunderson is Head of house shes unmarried.I think Frances Jones is Mary Jones the Boarders Grandaughter.
Mary Jones,Boarder,Widow,70,Bala
Frances Mary Jones,do Grandaughter,Bala
The do is under Boarder stands for ditto i think so Boarders Grandaughter.
Possible Marriage for Parents
Walter BC Jones to Mary F Knight in Oswestry Qtr Sept
1866 Vol 6a Page 1163
Welsh Lady