Aw, that's kinda sweet that she's so dependent on your sister.
If it makes you feel any better, our dogs are always fondest of the one who happens to be gone most, too--so it's not that she likes you less, just that I'll bet you're home more.
As for preparing, I'm not sure there's much you can do, barring having your sister totally ignore Mona until she leaves, and that would be emotionally draining for both of them! After your sister leaves, make sure you stick to your normal routine (dogs are comforted by predictable schedules) but add a new twist (maybe at walk time, walk in a different area than normal just to change things up; or when it's time to play, use a novel toy.) Don't push her, don't coddle her. Offer her usual treats, but if she won't take them, don't make a big deal about it. She'll come around soon enough.
Hope your mouth is feeling better soon, too!
