Kids need security so if leaving them once and awhile is what is causing the screaming, you need to start working on a plan to get that under control. You will come back and to a 2 or 3 year old, thats not always an easy concept to remember. Bribery can work sometimes and I don't mean spending money or buying ice cream, though that would work too sometimes lol.
But before you leave, while getting ready explain to them what is going to happem. Tell them "dDo you guys remember Sally (babysitter)? well she is going to com eover and this evening and visit you guys, Wouldn't that be fun? Maybe you can watch Shrek (bare with me lol) with her? THat would be soooo much fun wouldn't it. Then when the babysitter gets there, visit for a bit, son't run out the door and NEVER sneak out the back when they are not paying attention. After a 10 or 20 min. visit then tell them again that you are leaving in about 5 min. then when it's time to go, remind them of all the fun they are going to have and kiss and hug and we will see you in a bit. Then leave. Of course they will scream, but from my two year old she is much easier to deal with now. She only screams for a few minutes then calms right down to play.
Another idea would be to make it special for the kids by taking one to a grandparents to spend the night while the other stays home with the babysitter, then switch the next time. Give the child some one on one time with a relative they love and osmetimes when both kids are freaking out they feed off of eac other