I dont see that Emma regards looking after her father, however tedious he may be, as a tedious task. It is a diffuclt one certianly, and she's pleased that there are other people like Miss B and Mrs Goddard who can entertain him.. anad yes she is human, she does feel the strain of it sometimes but I see no evidence that she's "using" Miss B to keep him happy....
While she had Miss Taylor, she had a friend on hand who could give her companionship as well as helping to keep him happy - thats what she misses now that Miss T is married....