We do not have any way for the children to watch videos. This is good, because at this stage, if I had it as an option, I would abuse it. So these are some things we do when we've all had it and I must find something to keep them busy or lose my sanity.
First and foremost, if the weather is at all agreeable, we go outside. I don't know why this works, but it does. Take two cranky, fretful children outside and the baby will sit happily in the grass for half an hour, looking at a pinecone, while the toddler empties and fills a dumptruck or watches the cars go by. (Not that they are always good outside, but it seems to be a lot easier than being good inside.) Even sitting on the porch and watching the rain is better than nothing. We have appropriated the ten-foot strip of communal grass between our building and the sidewalk and treat it as our own.
If D2 is reasonably well fed and has had sufficient human contact, I fill a large, sturdy basket with an assortment of reasonably safe things–a block, a beanbag, an outgrown shoe, an empty bottle, a scrap of fabric, whatever comes to hand. He will often happily sit or roll around and empty it, contemplating the various items, for half an hour.
For D1, my standby activity is either a sinkful of water or a pan full of flour, and an assortment of measuring cups, spoons, or plastic dishes. Yes, this makes a mess. But I probably needed to scrub the kitchen floor anyway. If I get distracted and leave the dishes or cooking midway, she will probably climb up and start doing this on her own.
For both of them, the bin of Duplos will keep them quiet for fifteen minutes while I vacuum the rest of the house so D2 doesn't eat too much hair.