I know it isn't always possible, but couldn't the baby sitter Do more activities with the kids??? Playdough, waterplay, reading stories, peek-a-boo with a blanket, stringing fruit loops or cheerios on a peice of dry spagetti stuck in a small marshmallow. Getting them outside or doing little fun exercises. It sounds like they only have trouble when they are on their own. She wouldn't have to play with both at once either if they weren't interested. Just be more involved. The kids could help her prepare lunch, or even help clean up a bit if you had 2 small little brooms,etc. I know they are only two, so their "helping" is less about actually getting something accomplished than just keeping them occupied and happy.
I would also ask her to chart when during the day the problem is the worst, before nap, before lunch?? are they getting enough to drink during the day, are they tired, that sort of thing. The beauty of an inhome babysitter is that she can change the schedule to meet the needs of the kids on a given day.
Good luck and just keep showing them the right way to behave, they'll get it, sooner or later.