Oh V.!
Sounds like your daughter is having trouble going from having everyone's attention to having to share it with her sister. I agree, there needs to be some kind of transition time to get your younger daughter back into the swing of things when her sis comes home.
As for the tantrums. All kids have a currency of some sort.... something they treasure, like, or just HAVE to have access to. Find out what that is. Often, if time out doesn't work... taking away that currency when they misbehave does. It's the equivalent of their world falling apart basically. Kids quickly learn how far they can push the envelope...how long they have to cry or throw a tantrum until mommy and daddy give in. However, if the consequences are severe (in their minds) then you can modify the behavior. You don't have to resort to spanking and such. You just need to find out what it is that your daughter REALLY needs to have in her life (a stuffed toy, a particular snack, whatever it is) and then take it away when she misbehaves. Of course giving it back when she is acting appropriately again. It's kind of like taking the car keys away from an older teenager who hates to be driven around by their parents. ;-)
Good luck!