1 No, although it probably is peaceful as well - it's more a sense of indulging an error or incompetence or potentially annoying behaviour, 'putting up with it'. Perhaps I've guessed the context wrong, but is it Peggotty being maternal to young David?
2 It's not an exceptional. The focus was on the event. It's usually sad to say goodbye to one's mother, but in this case David is thinking how sad the event was.