I agree. I think a talking to would be in order. I do remember meeting your pet sitter at the cat show recently and you both seemed to have a good repoir. However, I do think it's a little far to comment on house cleaning (which is irrelevant) and the (aggressive) behaviors. The only things I would want to know about were any medical problems or anything that seemed really out of the ordinary. Maybe something funny that happened would be a nice interlude. What was the comment on a mess in the litterbox all about? That's where they're supposed to be, isn't it?? I would much prefer it there as opposed to on the floor or on my bed, you know?? LOL
Plus, I'm sure the cats do react differently when someone else is in the house and while we're away.

Since she knew Sassy and Cassy, she does seem to be making these comments based on how she knew Cassy then. That was a major loss for Cassy(and you), and yes...it could have changed his personality a bit, along with the fact that he is a little older now too.
While growing up, we had Socks(who is still with my parents) and Winston and they were like brothers. They got along great, played all the time and even slept together. When Winston died suddenly, Socks was never the same, and he never played the same with any other cat. That's just how it is. No other cat could replace Winston. Cassy and Livvy may just not have that same bond as Cassy and Sassy had. Who knows. It's really none of the cat sitter's business. She needs to give Livvy more of a chance. After all, they co-habitate just fine with you in the house, and they might just be a little more agitated when you're gone and a sitter is present.
Maybe have her come to your home so you could have your talk, but also have her interact with Livvy a bit. When I met Cassy and Livvy, I don't see how anyone could dislike either of them! Good luck and go with your instincts. Do let us know what happens and hugs to you and your kids!