I haven't had to deal with this type of situation, but I've been reading The Cat Site for a while, and I do work with ferals now.
It sounds like what is happening to me is that Auxana is exerting her authority as the alpha cat, and Sarah is too shy to fight for any upstairs territory, and so she retreats back downstairs, where she doesn't have to defend her territory. It is a little difficult to tell from your post, but could that be what's up?
Cats are very
territorial, and are driven by smell.
IF they were sharing the same territory, things you could do to help would be - play with Auxana first, feed Auxana first, etc. Height also plays a very important part in cat hierarchies. Do you have a cat tree? Or a shelf they can get to you can clear out? Sometimes just having a space where the Alpha can get up above everyone else helps the dominance aggression.
You can take a towel, and rub it all over Auxana. Then rub Auxana's scent on Sarah. Problem is, Sarah has no reason to go upstairs. She'll probably just give herself a bath to redistribute her own scent all over herself.
To introduce cats to each other, the usual recommendation is to keep the new kitty in a separate room to get everyone comfortable and used to the idea someone else is around - but they don't have to interact. Then you slowly introduce them to each other - open the door a crack (supervised) so they can see and smell each other. Then when "meeting" each other, rub the smell of the alpha (Auxana) on Sarah by using a towel to rub Auxana, then rub that on Sarah. Then supervise the actual meeting - and don't interefere unless someone is actually getting hurt. There will be arched backs, flat ears, hissing. But unless claws are out, let them work it out or they won't ever live together or enjoy playing with each other. They have to get their hierarchy in shape.
I don't know if any of this helps, because it seems you have two territories going on! The only thing I've read that may help, is to take two towels, and rub Sarah's scent on one and Auxana's scent on another. Put the towel with Sarah's scent on it under the dish where Auxana eats, and put the towel with Auxana's scent on it under the dish where Sarah eats. This will help them get used to each other.
Other than that, I'm not sure! Have you tried a search for "introduc*" here? I'm not sure what you'll find, but give it a shot!