Why did Carmen apologise to Libby?

I think it's because she had jeans on and she knew how not-picky the gag was

Because Tibby was more sensitive after Bailey died so when she told her of her experience at her dad's, Tibby wasn't as sympathetic as usual. Carmen felt she wasn't on her side.

You meant Tibby, right?

Because Carmen was told by Tibby's mom about Bailey so she realized that Tibby is going through a tough time too because of Bailey.

Because she had no reason to yell at Libby. Carmam was angry at her dad and taking it out on her.

Well her brand is Be Kind but shes anything but.