The impression I get from reading this page is that Jane Austen is making ridicule of Mrs Musgrove's sudden sorrow for the loss of a perfectly worthless child who had been "scarcely at all regretted".

Even the expression "he was grown so steady, and such an excellent correspondent" is meant to be ironic, when you think that Dick only wrote two disinterested letters, not particularly brilliant either.

So now Mrs Musgrove is grieving all of a sudden for the loss of this "thick-headed, unfeeling, unprofitable Dick Musgrove, who had never done any thing to entitle himself to more than the abbreviation of his name, living or dead" and although her feelings are NOW exceedingly affected, still it does sound a little...peculiar...that she should think about him only now and only because Capt. Wentworth's name reminded her of her son. She might otherwise have spent many years more without ever thinking of him at all.

Therefore I put the "infamous" passage in this context of general irony (sarcasm?): Mrs Musgrove if much more fitted for laughter and good-humour, and she looks a little strange in this sudden burst of sorrow, although Jane Austen admits that, of course, everyone is entitled to grieve as much as they like.