Great posts.

I agree that Lady Middleton's coldness is a lack of interest (paired with showing very little effort). But this lack of interest is more than that Lady Middleton doesn't share the Dashwood sisters' interest in discussing literature and other subjects. I think Lady Middleton's lack of interest is rather that she doesn't have much interest in making conversation about anything (except to talk about her children).

This is from chapter 7:

Lady Middleton piqued herself upon the elegance of her table, and of all her domestic arrangements; and from this kind of vanity was her greatest enjoyment in any of their parties. But Sir John's satisfaction in society was much more real;

Lady Middleton enjoys hosting parties because of the satisfaction she gets from setting a nice table, etc. -- NOT from any enjoyment of having guests with whom to converse. I think JA makes that pretty clear in the passage I cited above.

Also, I don't think Marianne and Elinor dislike children in general; I think they are not particularly interested in or impressed with the Middleton children due to the children's lack of manners. We saw in ch. 6 how the Dashwoods showed a proper interest and attention in the eldest of the Middleton offspring:

Lady Middleton had taken the wise precaution of bringing with her their eldest child, a fine little boy about six years old, by which means there was one subject always to be recurred to by the ladies in case of extremity, for they had to inquire his name and age, admire his beauty, and ask him questions.