with Charles and Mary or with Capt. Wentworth.

I think she doesn't completely approve of Charles' and (especially) Mary's choice to leave the sick child, and I believe she wouldn't have left her own child in those conditions, but I can see nothing in the text to point out that she's angry with them. On the contrary she tries to reconcile Mary with the choice of leaving the child to the care of somebody else, which even she (Mary) must realise is, at the very least, peculiar.

And it doesn' seem to me that Anne is angry with Capt. Wentworth either. Of course she can't be pleased at the idea of his making himself agreeable to everybody but herself, but I can hardly suppose she would be pleased to see him sullen and low-spirited. She's just sad at how things have turned out.

Actually it is exactly the feelings that you call "weaknesses" that make Anne's character really round and human: all these complexities which go on in her mind make her real. I wouldn't love her more if she had a perfectly rational control over her emotions.