Have you tried giving the toddler something to do? A lot of the problem with young children "requiring constant attention" tends to just be a lack of things for them to pay attention to.

One way to try and mitigate it is by giving them a GBA or DS (preferably the former, because they're harder to break, and certainly not a 3DS for a variety of reasons). This also has the really neat benefit of helping them bootstrap reading skills.

Movies usually don't work, because anything that doesn't require you to move (even just your hands, like with a handheld console) will cause restlessness.

You can probably take a few hours at first to teach her how to pronounce letters and put them together if you haven't already, after they figure out how to read, they require significantly less immediate attention.