I've always had the intuition that Alexia and MC are not close either. But's not based on anything specific...just a feeling that they have nothing in common and that there might be jealousies/rivalries.
Alexia has the most gorgeous children!
I have the exact same sense, also based on nothing more than an impression from pictures. Alexia strikes me as someone very down-to-earth, sporty, easy-going, and confident enough in her station in life that she doesn't have to show off. (Much like the Spanish infantas.)
MC's interests seem more high-profile and sophisticated -- she's got a more "manufactured" looking lifestyle.
And, yes, Alexia's kids are adorable. Some of the pictures of her older daughter as a toddler reminded me of pix of Liza Minnelli at the same age (those big eyes!), but I think she's headed for a more classically beautiful look than Liza has. (Never mind the looks -- if she gets talent like Liza has, she'll be even luckier!)